solvability of one dimensional phase field systems associated with grain boundary motion in this paper a coupled system of two parabolic equations subject to the homogeneous neumann boundary conditions and initial conditions is considered as a one dimensional version of the phase field system of grain boundary motion proposed by kobayashi et al phys d 140 1 2 141 150 2000 and free boundary problems theory and applications gakuto international series mathematical sciences and applications vol 14 gakkotosho tokyo 2000 the system presented includes some non standard situations and these non standard situations come from a weighted total variation constructed from the governing free energy the main objective of this paper is to define a solution to our system which is valid for the focused non standard situations this objective is achieved by proving the main theorem which is concerned with the existence of solutions to our system

an approach for finding the most preferred alternative in the presence of multiple criteria abstract an interactive approach for discrete multiple criteria decision making problems is developed the approach requires the decision maker to compare pairs of presented alternatives these alternatives may be existing alternatives or dummy alternatives created from existing alternatives inferior alternatives are sequentially eliminated by either using the responses of the decision maker directly or by constructing cones of inferior solutions based on these responses the approach converges to the most preferred solution so long as the decision maker has a nondecreasing quasiconcave value function the aim is to keep the number of pairwise comparisons required of the decision maker as small as possible computational experience on randomly generated problems is reported and the results are compared with the results of similar approaches

some issues in measuring and reporting solution quality of interactive multiple objective programming procedures issues in measuring and reporting solution quality are examined when value functions are used in computational experiments of interactive multiple objective programming procedures they include value functions used weights assigned to the objective functions in the value functions the size of the efficient set and the number of objective functions the feasibility and existence of the ideal and nadir points are also discussed detailed examples are presented to demonstrate these issues neither the users nor in fact the researchers may discern these issues even though they have strong impacts on the reported solution qualities common practices in the computational experiments of interactive multiple objective programming procedures are reviewed

on the computational efficiency of multiple objective metaheuristics the knapsack problem case study abstract the paper describes a computational experiment which goal is to evaluate computational efficiency of three multiple objective evolutionary metaheuristics on the multiple objective multiple constraints knapsack problem the relative efficiency of the multiple objective algorithms is evaluated with respect to a single objective evolutionary algorithm ea we use a methodology that allows consistent evaluation of the quality of approximately pareto optimal solutions generated by both multiple and single objective metaheuristics then we compare computational efforts needed to generate solutions of approximately the same quality by the two kinds of methods the results indicate that computational efficiency of multiple objective eas deteriorates with the growth of the number of objectives furthermore significant differences in the performance of the three algorithms are observed

risk averse pde constrained optimization using the conditional value at risk uncertainty is inevitable when solving science and engineering application problems in the face of uncertainty it is essential to determine robust and risk averse solutions in this work we consider a class of pde constrained optimization problems in which the pde coefficients and inputs may be uncertain we introduce two approximations for minimizing the conditional value at risk cvar for such pde constrained optimization problems these approximations are based on the primal and dual formulations of cvar for the primal problem we introduce a smooth approximation of cvar in order to utilize derivative based optimization algorithms and to take advantage of the convergence properties of quadrature based discretizations for this smoothed cvar we prove differentiability as well as consistency of our approximation for the dual problem we regularize the inner maximization problem rigorously derive optimality conditions and demonstrate the consistency of our approximation furthermore we propose a

quasi concave density estimation maximum likelihood estimation of a log concave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum shannon entropy problem closely related maximum renyi entropy estimators that impose weaker concavity restrictions on the fitted density are also considered notably a minimum hellinger discrepancy estimator that constrains the reciprocal of the square root of the density to be concave a limiting form of these estimators constrains solutions to the class of quasi concave densities

optimality and invexity in optimization problems in banach algebras spaces abstract in this paper we introduce into nonsmooth optimization theory in banach algebras a new class of mathematical programming problems which generalizes the notion of smooth kt p r invexity in fact this paper focuses on the optimality conditions for optimization problems in banach algebras regarding the generalized kt p r invexity notion and kuhn tucker points

existence of solutions to quasi linear elliptic problems with generalized robin boundary conditions abstract we characterize the l q solvability of a class of quasi linear elliptic equations involving the p laplace operator with generalized nonlinear robin type boundary conditions on bad domains some uniqueness results are also given

topological sensitivity analysis for elliptic differential operators of order 2m abstract the topological derivative is defined as the first term of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of a singular domain perturbation it has applications in many different fields such as shape and topology optimization inverse problems image processing and mechanical modeling including synthesis and or optimal design of microstructures fracture mechanics sensitivity analysis and damage evolution modeling the topological derivative has been fully developed for a wide range of second order differential operators in this paper we deal with the topological asymptotic expansion of a class of shape functionals associated with elliptic differential operators of order 2m m 1 the general structure of the polarization tensor is derived and the concept of degenerate polarization tensor is introduced we provide full mathematical justifications for the derived formulas including precise estimates of remainders

characterization of invariant measures at the leading edge for competing particle systems we study systems of particles on a line which have a maximum are locally finite and evolve with independent increments quasi stationary states are defined as probability measures on the algebra generated by the gap variables for which joint distribution of gaps between particles is invariant under the time evolution examples are provided by poisson processes with densities of the form p d x e sx s dx with s 0 and linear superpositions of such measures we show that conversely any quasi stationary state for the independent dynamics with an exponentially bounded integrated density of particles corresponds to a superposition of poisson processes with densities p dx e sx s dx with s 0 restricted to the relevant algebra among the systems for which this question is of some relevance are spin glass models of statistical mechanics where the point process represents the collection of the free energies of distinct pure states the time evolution corresponds to the addition of a spin variable and the poisson measures described above correspond to the so called rem states

the parisi formula in this chapter we prove the parisi formula which gives the limiting value of the free energy per site for the sherrington kirkpatrick model at each temperature starting with the famous result of guerra that the parisi formula provided a bound for this free energy we make full use of poisson dirichlet cascades we then use the same techniques to prove in a strong sense that in presence of an external field the overlaps are positive

dynamic multi source x ray tomography using a spacetime level set method a novel variant of the level set method is introduced for dynamic x ray tomography the target is allowed to change in time while being imaged by one or several source detector pairs at a relatively high frame rate the algorithmic approach is motivated by the results in 22 showing that the modified level set method can tolerate highly incomplete projection data in stationary tomography furthermore defining the level set function in spacetime enforces temporal continuity in the dynamic tomography context considered here the tomographic reconstruction is found as a minimizer of a nonlinear functional the functional contains a regularization term penalizing the l 2 norms of up to n derivatives of the reconstruction the case n 1 is shown to be equivalent to a convex tikhonov problem that has a unique minimizer for n 2 the existence of a minimizer is proved under certain assumptions on the signal to noise ratio and the size of the regularization parameter numerical examples with both simulated and measured dynamic x ray data are included and the proposed method is found to yield reconstructions superior to standard methods such as fbp or non negativity constrained tikhonov regularization and favorably comparable to those of total variation regularization furthermore the methodology can be adapted to a wide range of measurement arrangements with one or more x ray sources

interquad an interactive quad tree based procedure for solving the discrete alternative multiple criteria problem abstract in this paper an interactive procedure based upon a data structure called a quad tree is developed for solving the discrete alternative multiple criteria problem called interquad the procedure has been designed with large discrete alternative problems in mind interquad takes advantage of the ability of a quad tree to identify store and retrieve nondominated criterion vectors then the user interacts with the nondominated criterion vectors stored in the quad tree in a fashion similar to that of the combined tchebycheff aspiration criterion vector procedure of steuer silverman and whisman

on ruelle s probability cascades and an abstract cavity method we construct in this work a markov process which describes a clustering mechanism through which equivalence classes on are progressively lumped together this clustering process gives a new description of ruelle s continuous probability cascades it also enables to introduce an abstract cavity method which mimicks certain features of the cavity method developed by physicists in the context of the sherrington kirkpatrick model

random overlap structures properties and applications to spin glasses random overlap structures rost s are random elements on the space of probability measures on the unit ball of a hilbert space where two measures are identified if they differ by an isometry in spin glasses they arise as natural limits of gibbs measures under the appropriate algebra of functions we prove that the so called cavity mapping on the space of rost s is continuous leading to a proof of the stochastic stability conjecture for the limiting gibbs measures of a large class of spin glass models similar arguments yield the proofs of a number of other properties of rost s that may be useful in future attempts at proving the ultrametricity conjecture lastly assuming that the ultrametricity conjecture holds the setup yields a constructive proof of the parisi formula for the free energy of the sherrington kirkpatrick model by making rigorous a heuristic of aizenman sims and starr

a multiple criteria method for choosing among discrete alternatives abstract an interactive method is presented for solving a discrete alternative multiple criteria problem under certainty the method is based on the approach of zionts and wallenius a computer program embodying the method has been written and the results to date have been favorable extensions to the case in which some of the criteria are not readily quantifiable are also considered

can a linear value function explain choices an experimental study abstract we investigate in a simple bi criteria experimental study whether subjects are consistent with a linear value function while making binary choices many inconsistencies appeared in our experiment however the impact of inconsistencies on the linearity vs non linearity of the value function was minor moreover a linear value function seems to predict choices for bi criteria problems quite well this ability to predict is independent of whether the value function is diagnosed linear or not inconsistencies in responses did not necessarily change the original diagnosis of the form of the value function our findings have implications for the design and development of decision support tools for multiple criteria decision making problems

notes on the polynomial identities in random overlap structures in these notes we review first in some detail the concept of random overlap structure rost applied to fully connected and diluted spin glasses we then sketch how to write down the general term of the expansion of the energy part from the boltzmann rost for the sherrington kirkpatrick model and the corresponding term from the ramost which is the diluted extension suitable for the viana bray model

an interactive evolutionary metaheuristic for multiobjective combinatorial optimization we propose an evolutionary metaheuristic for multiobjective combinatorial optimization problems that interacts with the decision maker dm to guide the search effort toward his or her preferred solutions solutions are presented to the dm whose pairwise comparisons are then used to estimate the desirability or fitness of newly generated solutions the evolutionary algorithm comprising the skeleton of the metaheuristic makes use of selection strategies specifically designed to address the multiobjective nature of the problem interactions with the dm are triggered by a probabilistic evaluation of estimated fitnesses while memory structures with indifference thresholds restrict the presentation of solutions resembling those that have already been rejected the algorithm has been tested on a number of random instances of the multiobjective knapsack problem mokp and the multiobjective spanning tree problem most simulation results indicate that the algorithm requires only a small number of comparisons to be made for satisfactory solutions to be found

broken replica symmetry bounds in the mean field spin glass model by using a simple interpolation argument in previous work we have proven the existence of the thermodynamic limit for mean field disordered models including the sherrington kirkpatrick model and the derrida p spin model here we extend this argument in order to compare the limiting free energy with the expression given by the parisi ansatz and including full spontaneous replica symmetry breaking our main result is that the quenched average of the free energy is bounded from below by the value given in the parisi ansatz uniformly in the size of the system moreover the difference between the two expressions is given in the form of a sum rule extending our previous work on the comparison between the true free energy and its replica symmetric sherrington kirkpatrick approximation we give also a variational bound for the infinite volume limit of the ground state energy per site

generating a representative subset of the nondominated frontier in multiple criteria decision making in this paper we address the problem of generating a discrete representation of the nondominated frontier in multiple objective linear problems we find a surface that approximates the shape of the nondominated frontier utilizing the surface we generate a set of discrete points that is representative of the frontier our experience on randomly generated problems demonstrates that the approach performs well in terms of both the quality of the representation and the computation time

generalized invexity of nonsmooth functions abstract in this paper the concepts of weak invexity and weak quasi invexity are introduced and the relations among several kinds of generalized invexity are studied for nonsmooth functions by means of the properties of limiting subdifferentials in addition the relations between generalized invexity of a nonsmooth function and generalized invariant monotonicity of its limiting subdifferential mapping are researched our results here are an extension and generalization of those presented by m soleimani damaneh

on generalized convexity in asplund spaces abstract in this paper some properties of nonsmooth quasiconvex and pseudoconvex functions in weakly compactly generated asplund spaces are proved

spin glass computations and ruelle s probability cascades we study the parisi functional appearing in the parisi formula for the pressure of the sk model as a functional on ruelle s probability cascades rpc computation techniques for the rpc formulation of the functional are developed they are used to derive continuity and monotonicity properties of the functional retrieving a theorem of guerra we also detail the connection between the aizenman sims starr variational principle and the parisi formula as a final application of the techniques we rederive the almeida thouless line in the spirit of toninelli but relying on the rpc structure

a remark on the infinite volume gibbs measures of spin glasses in this note we point out that infinite volume gibbs measures of spin glass models on the hypercube can be identified as random probability measures on the unit ball of a hilbert space this simple observation follows from a result of dovbysh and sudakov on weakly exchangeable random matrices limiting gibbs measures can then be studied as single well defined objects this approach naturally extends the space of random overlap structures as defined by aizenman et al we discuss the ruelle probability cascades and the stochastic stability within this framework as an application we use an idea of parisi and talagrand to prove that if a sequence of finite volume gibbs measures satisfies the ghirlanda guerra identities then the infinite volume measure must be singular as a measure on a hilbert space

learning with boundary conditions kernel machines traditionally arise from an elegant formulation based on measuring the smoothness of the admissible solutions by the norm in the reproducing kernel hilbert space rkhs generated by the chosen kernel it was pointed out that they can be formulated in a related functional framework in which the green s function of suitable differential operators is thought of as a kernel in this letter our own picture of this intriguing connection is given by emphasizing some relevant distinctions between these different ways of measuring the smoothness of admissible solutions in particular we show that for some kernels there is no associated differential operator the crucial relevance of boundary conditions is especially emphasized which is in fact the truly distinguishing feature of the approach based on differential operators we provide a general solution to the problem of learning from data and boundary conditions and illustrate the significant role played by boundary conditions with examples it turns out that the degree of freedom that arises in the traditional formulation of kernel machines is indeed a limitation which is partly overcome when incorporating the boundary conditions this likely holds true in many real world applications in which there is prior knowledge about the expected behavior of classifiers and regressors on the boundary

first order optimality conditions for elliptic mathematical programs with equilibrium constraints via variational analysis mathematical programs in which the constraint set is partially defined by the solutions of an elliptic variational inequality so called elliptic mpecs are formulated in reflexive banach spaces with the goal of deriving explicit first order optimality conditions amenable to the development of numerical procedures variational analytic concepts are both applied and further developed the paper is split into two main parts the first part concerns the derivation of conditions in which the lower level state constraints are assumed to be polyhedric sets this part is then completed by two examples the latter of which involves pointwise bilateral bounds on the gradient of the state the second part focuses on an important nonpolyhedric example namely when the lower level state constraints are presented by pointwise bounds on the euclidean norm of the gradient of the state a formula for the second order mosco epiderivative of the indicator function for this convex set is derived this result is then used to demonstrate the hadamard directional differentiability of the solution mapping of the variational inequality which then leads to the derivation of explicit strong stationarity conditions for this problem

higher order regularization based image restoration with automatic regularization parameter selection abstract poisson and multiplicative rayleigh noises often appear in medical imaging such as x ray images positron emission tomography and ultrasound images in this study we propose novel variational models for removing poisson multiplicative rayleigh noise we make use of hybrid higher order total variation as the regularization terms of our proposed models to eliminate staircasing artifacts we also adopt the spatially adaptive parameter technique to adequately smooth homogenous regions while preserving the edges the spatially adaptive parameter selection is closely related to local constraints through a local expected value estimator we provide a convergence analysis including the existence and uniqueness of solution and the first order optimality conditions we apply the alternating direction method of multipliers for solving the proposed models numerical experiments demonstrate that our models exhibit a better performance than that of state of the art models in terms of edge preservation smoothness of the homogenous regions and various quality measures

the ipicea g a new hybrid evolutionary multi criteria decision making approach using the brushing technique various preference based multi objective evolutionary algorithms have been developed to help a decision maker search for his her preferred solutions to multi objective problems in most of the existing approaches the decision maker preferences are formulated either by mathematical expressions such as the utility function or simply by numerical values such as aspiration levels and weights however in some sense a decision maker may find it easier to specify preferences visually by drawing rather than using numbers this paper introduces such a method namely the brushing technique using this technique the decision maker can specify his her preferences easily by drawing in the objective space combining the brushing technique with one existing algorithm picea g we present a novel approach named ipicea g for an interactive decision making the performance of ipicea g is tested on a set of benchmark problems and is shown to be good

zero one programming with multiple criteria abstract the study of multiple criteria problems is not new but during the last seventeen years more and more study has been done in this area the study of 0 1 multiple criteria problems started much later than the study of continuous multiple criteria problems some of the earliest works on 0 1 problems with multiple criteria was first presented in 1973 quite a few solution methods have been developed since then especially during the last seven years in this paper most of these methods and some applications will be treated

an interactive branch and bound algorithm for multiple criteria optimization we present a new interactive algorithm for multiple criteria optimization the algorithm is of the branch and bound type and differs from previous interactive algorithms in several ways first the field of application is wider because it applies to two important classes of multiple criteria decision problems those for which the feasible set is convex and those for which the feasible set is discrete secondly the algorithm does not require a great deal from the decision maker he is merely required to indicate his preference between two vectors whenever the algorithm so demands

evaluation of nondominated solution sets for k objective optimization problems an exact method and approximations abstract integrated preference functional ipf is a set functional that given a discrete set of points for a multiple objective optimization problem assigns a numerical value to that point set this value provides a quantitative measure for comparing different sets of points generated by solution procedures for difficult multiple objective optimization problems we introduced the ipf for bi criteria optimization problems in carlyle w m fowler j w gel e kim b 2003 quantitative comparison of approximate solution sets for bi criteria optimization problems decision sciences 34 1 63 82 as indicated in that paper the computational effort to obtain ipf is negligible for bi criteria problems for three or more objective function cases however the exact calculation of ipf is computationally demanding since this requires k 3 dimensional integration in this paper we suggest a theoretical framework for obtaining ipf for k 3 objectives the exact method includes solving two main sub problems 1 finding the optimality region of weights for all potentially optimal points and 2 computing volumes of k dimensional convex polytopes several different algorithms for both sub problems can be found in the literature we use existing methods from computational geometry i e triangulation and convex hull algorithms to develop a reasonable exact method for obtaining ipf we have also experimented with a monte carlo approximation method and compared the results to those with the exact ipf method

solving the discrete multiple criteria problem using convex cones an interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi concave increasing utility or value function the method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions the maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker responses are used to eliminate alternatives using convex cones based on expressed preferences and then a new set of weights is found that satisfies the indicated preferences the requisite theory and proofs as well as a detailed numerical example are included in addition the results of some computational experiments to test the effectiveness of the method are described

preference ranking of discrete multiattribute instances abstract this paper presents a procedure for preference ranking of discrete multiattribute instances based on the observations that 1 a difficult question could be answered in terms of answers to a sequence of easier ones 2 in general the decision maker s preferences can easily be expressed only relative to pairs of instances that differ over one attribute and 3 the decision maker is able and willing to express his uncertainty regarding a quantity via a subjective probability distribution the procedure is illustrated through a hypothetical situation

on the density of classes of closed convex sets with pointwise constraints in sobolev spaces abstract for a banach space x of r m valued functions on a lipschitz domain let k x x be a closed convex set arising from pointwise constraints on the value of the function its gradient or its divergence respectively the main result of the paper establishes under certain conditions the density of k x 0 in k x 1 where x 0 is densely and continuously embedded in x 1 the proof is constructive utilizes the theory of mollifiers and can be applied to sobolev spaces such as h 0 div and w 0 1 p in particular it is also shown that such a density result cannot be expected in general

a bundle free implicit programming approach for a class of elliptic mpecs in function space using a standard first order optimality condition for nonsmooth optimization problems a general framework for a descent method is developed this setting is applied to a class of mathematical programs with equilibrium constraints in function space from which a new algorithm is derived global convergence of the algorithm is demonstrated in function space and the results are then illustrated by numerical experiments

asymptotic behavior of nonautonomous monotone and subgradient evolution equations in a hilbert setting h we study the asymptotic behavior of the trajectories of nonautonomous evolution equations dot x t a t x t ni 0 where for each t geq 0 a t h rightrightarrows h denotes a maximal monotone operator we provide general conditions guaranteeing the weak ergodic convergence of each trajectory x cdot to a zero of a limit maximal monotone operator a infty as the time variable t tends to infty the crucial point is to use the brezis haraux function or equivalently the fitzpatrick function to express at which rate the excess of mathrm gph a infty over mathrm gph a t tends to zero this approach gives a sharp and unifying view of this subject in the case of operators a t partial phi t which are subdifferentials of proper closed convex functions phi t we show convergence results for the trajectories then we specialize our results to multiscale evolution equations and obtain asymptotic properties of hierarchical minimization and selection of viscosity solutions illustrations are given in the field of coupled systems and partial differential equations

the use of domains in multicriteria decision making abstract this paper describes a domain criterion for a multicriteria problem given decision maker it then outlines possibilities for aggregating individual preference structures in the case of multiple decision makers

an interactive weight space reduction procedure for nonlinear multiple objective mathematical programming to make a decision that is defined by multiple conflicting objectives it is necessary to know the relative importance of the different objectives in this paper we present an interactive method and the underlying theory for solving multiple objective mathematical programming problems defined by a convex feasible region and concave continuously differentiable objective functions the relative importance of the different objectives for a decision maker is elicited by using binary comparisons of objective function vectors the method is cognitively easy to use and in test problems has rapidly converged to an optimal solution

existence uniqueness and stability of solutions of generalized tikhonov phillips functionals abstract the tikhonov phillips method is widely used for regularizing ill posed inverse problems mainly due to the simplicity of its formulation as an optimization problem the use of different penalizers in the functionals associated to the corresponding optimization problems has originated a variety of other methods which can be considered as variants of the traditional tikhonov phillips method of order zero such is the case for instance of the tikhonov phillips method of order one the total variation regularization method etc in this article we find sufficient conditions on the penalizers in generalized tikhonov phillips functionals which guarantee existence uniqueness and stability of the minimizers the particular cases in which the penalizers are given by the bounded variation norm by powers of seminorms and by linear combinations of powers of seminorms associated to closed operators are studied several examples are presented and a few results on image restoration are shown

pruning of decision alternatives in multiple criteria decision making based on the uta method for estimating utilities abstract a new interactive method for the progressive elimination of elements from a finite set of decision alternatives is proposed a sequence of alternatives is presented to the decision maker who places each new alternative presented in rank order relative to the earlier alternatives evaluated this ranking of elements in a subset of the decision space is used to eliminate other alternatives from further consideration the approach is broadly based on the uta method for utility assessment the emphasis is not however on assessing a utility function as such instead the class of utility functions is used to eliminate elements of the decision space when the optimality of such elements is inconsistent with the presumed properties of the utility function and the rank orderings given in this way the decision maker need only evaluate a relatively small subset of the decision space before all remaining alternatives are eliminated the new procedure is illustrated by two numerical examples

finite element error estimates in non energy norms for the two dimensional scalar signorini problem this paper is concerned with error estimates for the piecewise linear finite element approximation of the two dimensional scalar signorini problem on a convex polygonal domain varomega using a cea type lemma a supercloseness result and a non standard duality argument we prove w 1 p varomega l infty varomega w 1 infty varomega and h 1 2 partial varomega error estimates under reasonable assumptions on the regularity of the exact solution and l p varomega error estimates under comparatively mild assumptions on the involved contact sets the obtained orders of convergence turn out to be optimal for problems with essentially bounded right hand sides our results are accompanied by numerical experiments which confirm the theoretical findings

aspiration level approach in stochastic mcdm problems the paper considers a discrete stochastic multiple criteria decision making problem this problem is defined by a finite set of actions a a set of attributes x and a set of evaluations of actions with respect to attributes e in stochastic case the evaluation of each action with respect to each attribute takes form of a probability distribution thus the comparison of two actions leads to the comparison of two vectors of probability distributions in the paper a new procedure for solving this problem is proposed it is based on three concepts stochastic dominance interactive approach and preference threshold the idea of the procedure comes from the interactive multiple objective goal programming approach the set of actions is progressively reduced as the decision maker specifies additional requirements at the beginning the decision maker is asked to define preference threshold for each attribute next at each iteration the decision maker is confronted with the set of considered actions if the decision maker is able to make a final choice then the procedure ends otherwise he she is asked to specify aspiration level a didactical example is presented to illustrate the proposed technique

an interactive approach for placing alternatives in preference classes abstract in this paper we consider the multiple criteria decision making problem of partitioning alternatives into preference classes we develop an interactive procedure based on the assumption that the decision maker dm has a linear utility function the approach requires the dm to place an alternative in a preference class from time to time based on the preference information derived from the dm s placement as well as from dominance and linearity we try to place other alternatives we present results on the performance of the algorithm applied to four different sets of alternatives

dual cone approach to convex cone dominance in multiple criteria decision making abstract in a paper published in management science in 1984 korhonen wallenius and zionts presented the idea and method based on convex cone dominance in the discrete multiple criteria decision making framework in our current paper we revisit the old idea from a new standpoint and provide the mathematical theory leading to a dual cone based approach to solving such problems our paper makes the old results computationally more tractable the results provided in the present paper also help extend the theory

a sequential minimization technique for elliptic quasi variational inequalities with gradient constraints a class of nonlinear elliptic quasi variational inequality qvi problems with gradient constraints in function space is considered problems of this type arise for instance in the mathematical description of the magnetization of superconductors in problems in elastoplasticity or in electrostatics as well as in game theory the paper addresses the iterative solution of the qvis by a sequential minimization technique relying on the repeated solution of variational inequality type problems a monotone operator theoretic approach is developed which does not resort to mosco convergence as is often done in connection with existence analysis for qvis for the numerical solution of the qvis a penalty approach combined with a semismooth newton iteration is proposed the paper ends with a report on numerical tests involving the p laplace operator and various types of nonlinear constraints

characterization of nonsmooth quasiconvex and pseudoconvex functions this paper characterizes the nonsmooth quasiconvex and pseudoconvex functions using the properties of limiting subdifferentials

error estimate for godunov approximation of locally constrained conservation laws we consider a model of traffic flow with unilateral constraint on the flux introduced by colombo and goatin j differential equations 234 2007 pp 654 675 for which the convergence of numerical approximation using monotone finite volume schemes has been performed by andreianov goatin and seguin numer math 115 2010 pp 609 645 we derive for this problem a new rm bv estimate and make use of it to provide an error estimate for the godunov approximation of the problem of order h 1 3 that is improved into the optimal order h 1 2 under a reasonable assumption numerical experiments are then provided to illustrate the optimality of the result

a mean value theorem in asplund spaces abstract in this paper a nonsmooth mean value theorem in asplund spaces under invexity is provided

asymmetric poincare inequalities and solvability of capillarity problems abstract in this paper we first establish an asymmetric version of the poincare inequality in the space of bounded variation functions and then basically relying on this result we discuss the existence the non existence and the multiplicity of bounded variation solutions of a class of capillarity problems with asymmetric perturbations

monte carlo simulation techniques for group decision making with incomplete information abstract in this paper we deal with group decision making problems where several decision makers elicit their own preferences separately the decision makers preferences are quantified using a decision support system which admits incomplete information concerning the decision makers responses to the questions they are asked consequently each decision maker proposes classes of utility functions and attribute weight intervals for the different attributes we introduce an approach based on monte carlo simulation techniques for aggregating decision maker preferences that could be the starting point for a negotiation process if necessary the negotiation process would basically involve the decision maker tightening the imprecise component utilities and weights to output more meaningful results and achieve a consensus alternative we focus on how attribute weights and the component utilities associated with a consequence are randomly generated in the aggregation process taking into account the decision makers preferences i e their respective attribute weight intervals and classes of utility functions finally an application to the evaluation of intervention strategies for restoring a radionuclide contaminated lake illustrates the usefulness and flexibility of this iterative process

laplacian eigenproblems on product regions and tensor products of sobolev spaces abstract characterizations of eigenvalues and eigenfunctions of the laplacian on a product domain p 1 2 are obtained when zero dirichlet robin or neumann conditions are specified on each factor then the eigenfunctions on p are precisely the products of the eigenfunctions on the sets 1 2 separately there is a related result when steklov boundary conditions are specified on 2 these results enable the characterization of h 1 p and h 0 1 p as tensor products and descriptions of some orthogonal bases of the spaces a different characterization of the trace space of h 1 p is found

a branching random walk seen from the tip we show that all the time dependent statistical properties of the rightmost points of a branching brownian motion can be extracted from the traveling wave solutions of the fisher kpp equation the distribution of all the distances between the rightmost points has a long time limit which can be understood as the delay of the fisher kpp traveling waves when the initial condition is modified the limiting measure exhibits the surprising property of superposability the statistical properties of the distances between the rightmost points of the union of two realizations of the branching brownian motion shifted by arbitrary amounts are the same as those of a single realization we discuss the extension of our results to more general branching random walks

convergence of a nonlinear entropy diminishing control volume finite element scheme for solving anisotropic degenerate parabolic equations in this paper we propose and analyze a control volume finite elements cvfe scheme for solving possibly degenerated parabolic equations this scheme does not require the introduction of the so called kirchhoff transform in its definition we prove that the discrete solution obtained emph via the scheme remains in the physical range and that the natural entropy of the problem decreases with time the convergence of the method is proved as the discretization steps tend to 0 finally numerical examples illustrate the efficiency of the method

on boundary detachment phenomena for the total variation flow with dynamic boundary conditions abstract we combine the total variation flow suitable for crystal modeling and image analysis with the dynamic boundary conditions we analyze the behavior of facets at the parts of the boundary where these conditions are imposed we devote particular attention to the radially symmetric data we observe that the boundary layer detachment actually can happen at concave parts of the boundary

interactive approaches for discrete alternative multiple criteria decision making with monotone utility functions in this paper we develop interactive approaches for the discrete alternative multiple criteria decision making problem we develop an algorithm that finds the most preferred alternative of a decision maker dm assuming only that the dm has a monotonic utility function the algorithm divides the criteria space into a number of smaller subspaces and then uses the ideal points of these subspaces to eliminate alternatives we also develop a more efficient version of the algorithm for the more restrictive case of a monotonic quasiconcave utility function we present favorable computational results in terms of the required number of pairwise comparisons for both versions of the algorithm we then develop a general algorithm that first identifies the type of the dm s utility function and then employs the approach that is compatible with the identified utility function type we also present computational results for the general algorithm

testing the efficiency of pairwise comparison methods in discrete multiple criteria problems we test the efficiency of two pairwise comparison methods the methods studied are salminen s piecewise linear prospect theory plp method and the convex cone method by korhonen wallenius and zionts kwz the plp method is based on a piecewise linear difference function the kwz method assumes a quasi concave utility or value function these methods are tested using randomly generated data sets with 50 100 150 and 200 alternatives and from 2 up to 6 criteria the dm s preference statements are simulated using linear quadratic and chebycheff value functions and piecewise linear difference functions both methods lose their efficiency very rapidly with increasing number of criteria our results indicate that pairwise comparison methods are not as efficient as reported in literature

identifying conductivity in electrical impedance tomography with total variation regularization in this paper we investigate the problem of identifying the conductivity in electrical impedance tomography from one boundary measurement a variational method with total variation regularization is here proposed to tackle this problem we discretize the pde as well as the conductivity with piecewise linear continuous finite elements we prove the stability and convergence of this technique for the numerical solution we propose a projected armijo algorithm finally a numerical experiment is presented to illustrate our theoretical results

decision making with incomplete information abstract decision situations with incomplete information are characterized by a decision maker without a precisely defined stable preference structure by probability distributions not known completely or by an inexact evaluation of consequences within the paper a general framework for decision making with incomplete information is presented which shows how to solve problems from descriptive as well as prescriptive decision theory based on this framework an overview of existing methods which are particularly suitable for handling incomplete information is given

variational method for multiple parameter identification in elliptic pdes abstract in the present paper we investigate the inverse problem of identifying simultaneously the diffusion matrix source term and boundary condition in the neumann boundary value problem for an elliptic partial differential equation pde from a measurement data which is weaker than required of the exact state a variational method based on energy functions with tikhonov regularization is here proposed to treat the identification problem we discretize the pde with the finite element method and prove the convergence as well as analyze error bounds of this approach

young measure quasi static damage evolution an existence result for the quasi static evolution of incomplete damage in elastic materials is presented the absence of gradient terms in the damage variable causes a critical lack of compactness therefore the analysis is developed in the framework of young measures where a notion of solution is defined presenting some improvements with respect to previous contributions the main new feature in the proof of the existence result regards a delicate construction of the joint recovery sequence

a progressive algorithm for modeling and solving multiple criteria decision problems we consider a decision maker dm who has a set of possible decision alternatives from which one a best is to be chosen however all decision alternatives are not at the dm s disposal initially nor is full knowledge of his her utility value function therefore the dm evaluates only the available subset of all decision alternatives from which he she chooses a most preferred one obviously this decision is not necessarily globally best two natural questions arise how good is the most preferred solution what are the chances of finding better solutions by considering additional alternatives we describe and illustrate a general progressive algorithm and the supporting theory for modeling and solving this problem when alternatives are introduced dynamically

rough sets theory for multicriteria decision analysis the original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation it operates on a data table composed of a set u of objects actions described by a set q of attributes its basic notions are indiscernibility relation on u lower and upper approximation of either a subset or a partition of u dependence and reduction of attributes from q and decision rules derived from lower approximations and boundaries of subsets identified with decision classes the original rough set idea is failing however when preference orders of attribute domains criteria are to be taken into account precisely it cannot handle inconsistencies following from violation of the dominance principle this inconsistency is characteristic for preferential information used in multicriteria decision analysis mcda problems like sorting choice or ranking in order to deal with this kind of inconsistency a number of methodological changes to the original rough sets theory is necessary the main change is the substitution of the indiscernibility relation by a dominance relation which permits approximation of ordered sets in multicriteria sorting to approximate preference relations in multicriteria choice and ranking problems another change is necessary substitution of the data table by a pairwise comparison table where each row corresponds to a pair of objects described by binary relations on particular criteria in all those mcda problems the new rough set approach ends with a set of decision rules playing the role of a comprehensive preference model it is more general than the classical functional or relational model and it is more understandable for the users because of its natural syntax in order to workout a recommendation in one of the mcda problems we propose exploitation procedures of the set of decision rules finally some other recently obtained results are given rough approximations by means of similarity relations rough set handling of missing data comparison of the rough set model with sugeno and choquet integrals and results on equivalence of a decision rule preference model and a conjoint measurement model which is neither additive nor transitive

strong stationarity for optimal control of the obstacle problem with control constraints we consider the distributed optimal control of the obstacle problem with control constraints since mignot proved in 1976 the necessity of a system which is equivalent to strong stationarity it has been an open problem whether such a system is still necessary in the presence of control constraints using moderate regularity of the optimal control and an assumption on the control bounds which is implied by u a 0 le u b quasi everywhere in omega in the case of an upper obstacle y le psi we can answer this question in the affirmative we also present counterexamples showing that strong stationarity may not hold if u a 0 or 0 le u b are violated an erratum is attached

interactive algorithms for a broad underlying family of preference functions abstract in multi criteria decision making approaches it is typical to consider an underlying preference function that is assumed to represent the decision maker s preferences in this paper we introduce a broad family of preference functions that can represent a wide variety of preference structures we develop the necessary theory and interactive algorithms for both the general family of the preference functions and for its special cases the algorithms guarantee to find the most preferred solution point of the decision maker under the assumed conditions the convergence of the algorithms are achieved by progressively reducing the solution space based on the preference information obtained from the decision maker and the properties of the assumed underlying preference functions we first demonstrate the algorithms on a simple bi criteria problem with a given set of available points we also test the performances of the algorithms on three criteria knapsack problems and show that they work well

regularized perimeter for topology optimization the perimeter functional is known to oppose serious difficulties when it has to be handled within a topology optimization procedure in this paper a regularized perimeter functional mbox per varepsilon defined for two and three dimensional domains is introduced on one hand the convergence of mbox per varepsilon to the exact perimeter when varepsilon tends to zero is proved on the other hand the topological differentiability of mbox per varepsilon for varepsilon 0 is analyzed these features lead to the design of a topology optimization algorithm suitable for perimeter dependent objective functionals several numerical results illustrate the method

use of convex cones in interactive multiple objective decision making one approach for solving decision problems involving multiple objectives is interactive optimization methods based on this approach assess the decision maker s preference structure interactively typically based on pairwise comparisons and tradeoffs and guide the search process toward identifying improved solutions a desirable feature of such approaches that is based on minimizing the preference information requirements is fast convergence toward this end the use of convex cones as a preference structure representation has been proposed in the literature in this work new theory is developed that aids in further reducing preference information requirements and improving convergence new cones termed p cones are developed the efficiencies of solution alternatives are evaluated with respect to the p cones and these are termed p cone efficiencies acceleration and early termination procedures that are based on these efficiencies are proposed the procedures are presented within a solution framework for solving multiple objective linear programming molp problems along with computational results

the full replica symmetry breaking in the ising spin glass on random regular graph in this paper we extend the full replica symmetry breaking scheme to the ising spin glass on a random regular graph we propose a new martingale approach that overcomes the limits of the parisi mezard cavity method providing a well defined formulation of the full replica symmetry breaking problem in random regular graphs finally we define the order parameters of the system and get a set of self consistency equations for the order parameters and the free energy we face up the problem only from a technical point of view the physical meaning of this approach and the quantitative evaluation of the solution of the self consistency equations will be discussed in next works

nonlinear stochastic partial differential equations with singular diffusivity and gradient stratonovich noise abstract we study existence and uniqueness of a variational solution in terms of stochastic variational inequalities svi to stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative stratonovich gradient type noise we derive a commutator relation for the unbounded noise coefficients in terms of a geometric killing vector condition the drift term is given by the total variation flow respectively by a singular p laplace type operator we impose nonlinear zero neumann boundary conditions and precisely investigate their connection with the coefficient fields of the noise this solves an open problem posed in barbu et al 2013 7 and barbu and rockner 2015 10

graphically structured value function compilation classical work on eliciting and representing preferences over multi attribute alternatives has attempted to recognize conditions under which value functions take on particularly simple and compact form making their elicitation much easier in this paper we consider preferences over discrete domains and show that for a certain class of simple and intuitive qualitative preference statements one can always generate compact value functions consistent with these statements these value functions maintain the independence structure implicit in the original statements for discrete domains these representation theorems are much more general than previous results however we also show that it is not always possible to maintain this compact structure if we add explicit ordering constraints among the available outcomes

optimal profiles in a phase transition model with a saturating flux abstract it is well known that for the allen cahn equation the minimizing transition in an infinite cylinder r is one dimensional and unique up to a translation in the first variable we analyze in this paper the existence and symmetry of optimal profiles for transitions in a similar phase separation model with a saturating flux this amounts to consider transitions in the space of bv functions as we consider the area integral instead of the dirichlet energy to penalize the creation of wild interfaces

evaluation functions and decision conditions of three way decisions with game theoretic rough sets abstract three way decisions have been used over the years in many application areas the rough sets and its extensions provide useful approaches for three way decisions typically these approaches employ a single evaluation function or criterion to induce three way decisions when extending the rough set based three way decisions to multiple criteria decision making mcdm two issues are encountered the first issue is related to the construction and definition of aggregation mechanisms for dealing with differences in results of evaluation functions the second issue is related to the setting of choice structure for selecting the three types of decision choices in this article we consider the role and use of game theoretic rough set gtrs model to resolve and address these two issues the issue related to differences in evaluation functions is addressed with gtrs by implementing a game that considers multiple evaluation functions as game players the game theoretic analysis in the gtrs is employed to resolve the differences by determining a tradeoff between evaluation functions the issue related to choice structure is addressed by considering the conditions under which different game outcomes could constitute a game solution in particular the equilibrium analysis within games is used to construct the rules for three way decisions a demonstrative example is used to explain the use of the proposed approach the relationship between the proposed approach and the probabilistic rough sets is also discussed

convergence rates for total variation regularization of coefficient identification problems in elliptic equations ii abstract we investigate the convergence rates for total variation regularization of the problem of identifying i the coefficient q in the neumann problem for the elliptic equation div q u f in q u n g on ii the coefficient a in the neumann problem for the elliptic equation u a u f in u n g on r d d 1 when u is imprecisely given by z h 1 u z h 1 0 we regularize these problems by correspondingly minimizing the strictly convex functionals 1 2 q u q z 2 d x 1 2 q l 2 2 q and 1 2 u a z 2 d x 1 2 a u a z 2 d x 1 2 a l 2 2 a over admissible sets where u q u a is the solution of the first second neumann boundary value problem 0 is the regularization parameter taking the solutions of these optimization problems as the regularized solutions to the corresponding identification problems we obtain the convergence rates of them to the solution of the inverse problem in the sense of the bregman distance and in the l 2 norm under relatively simple source conditions without the smallness requirement on the source functions

entropic regularization of continuous optimal transport problems abstract we analyze continuous optimal transport problems in the so called kantorovich form where we seek a transport plan between two marginals that are probability measures on compact subsets of euclidean space we consider the case of regularization with the negative entropy with respect to the lebesgue measure which has attracted attention because it can be solved by the very simple sinkhorn algorithm we first analyze the regularized problem in the context of classical fenchel duality and derive a strong duality result for a predual problem in the space of continuous functions however this problem may not admit a minimizer which prevents obtaining primal dual optimality conditions we then show that the primal problem is naturally analyzed in the orlicz space of functions with finite entropy in the sense that the entropically regularized problem admits a minimizer if and only if the marginals have finite entropy we then derive a dual problem in the corresponding dual space for which existence can be shown by purely variational arguments and primal dual optimality conditions can be derived for marginals that do not have finite entropy we finally show gamma convergence of the regularized problem with smoothed marginals to the original kantorovich problem

a measure approximation for distributionally robust pde constrained optimization problems in numerous applications scientists and engineers acquire varied forms of data that partially characterize the inputs to an underlying physical system this data is then used to inform decisions such as controls and designs consequently it is critical that the resulting control or design is robust to the inherent uncertainties associated with the unknown probabilistic characterization of the model inputs in this paper we consider optimal control and design problems constrained by partial differential equations with uncertain inputs we do not assume a known probabilistic model for the inputs but rather we formulate the problem as a distributionally robust optimization problem where the outer minimization problem determines the control or design while the inner maximization problem determines the worst case probability measure that matches desired characteristics of the data we analyze the inner maximization problem in the space of measures and introduce a novel measure approximation technique bas