linear programming system identification the general nonnegative parameters case abstract by linear programming system identification we mean the problem of estimating the objective function coefficient vector and the technological coefficient matrix a for a linear programming system that best explains a set of input output vectors input vectors are regarded as available resources output vectors are compared to imputed optimal ones by a decisional efficiency measure and a likelihood function is constructed in an earlier paper we obtained results for a simplified version of the problem in this paper we propose a genetic algorithm approach for the general case in which and a are of arbitrary finite dimensions and have nonnegative components a method based on householder transformations and monte carlo integration is used as an alternative to combinatorial algorithms for the extreme points and volumes of certain required convex polyhedral sets the method exhibits excellent face validity for a published test data set in data envelopment analysis

a new monte carlo power method for the eigenvalue problem of transfer matrices we propose a new monte carlo method for calculating eigenvalues of transfer matrices leading to free energies and to correlation lengths of classical and quantum many body systems generally this method can be applied to the calculation of the maximum eigenvalue of a nonnegative matrix such that all the matrix elements of k are strictly positive for an integerk this method is based on a new representation of the maximum eigenvalue of the matrix as the thermal average of a certain observable of a many body system therefore one can easily calculate the maximum eigenvalue of a transfer matrix leading to the free energy in the standard monte carlo simulations such as the metropolis algorithm as test cases we calculate the free energies of the square lattice ising model and of the spin 1 2xy heisenberg chain we also prove two useful theorems on the ergodicity in quantum monte carlo algorithms or more generally on the ergodicity of monte carlo algorithms using our new representation of the maximum eigenvalue of the matrix

calculating some inverse linear programming problems in this paper we consider some inverse lp problems in which we need to adjust the cost coefficients of a given lp problem as less as possible so that a known feasible solution becomes the optimal one a method for solving general inverse lp problem including upper and lower bound constraints is suggested which is based on the optimality conditions for lp problems it is found that when the method is applied to inverse minimum cost flow problem or inverse assignment problem we are able to obtain strongly polynomial algorithms

finite size corrections and numerical calculations for long spin 1 2 heisenberg chains in the critical region leading and next to leading order finite size corrections to the ground and first excited states are calculated for the spin 1 2 anisotropic heisenberg model in the critical region the analytic results are compared to numerical data obtained for chains up to a length of n 1024 it is found that near the isotropic point the asymptotic region where the results obtained for n to infinity are applicable sets in at very large n values and for obtaining good accuracy in fitting the numerical data one has to take into account several correction terms even at large n 100 chain lengths

efficient algorithms for the inverse spanning tree problem the inverse spanning tree problem is to modify edge weights in a graph so that a given treet is a minimum spanning tree the objective is to minimize the cost of the deviation the cost of deviation is typically a convex function we propose algorithms here that are faster than all known algorithms for the problem our algorithm s run time for any convex inverse spanning tree problem iso nm log 2n for a graph onn nodes andm edges plus the time required to find the minima of then convex deviation functions this not only improves on the complexity of previously known algorithms for the general problem but also for algorithms devised for special cases for the case when the objective is weighted absolute deviation sokkalingam et al 1999 devised an algorithm with run timeo n2m log nc forc the maximum edge weight for the sum of absolute deviations our algorithm runs in timeo n2 logn matching the run time of a recent ahuja and orlin 2000 improvement for this case a new algorithm for bipartite matching in path graphs is reported here with complexity ofo n1 5 logn this leads to a second algorithm for the sum of absolute deviations running ino n1 5 logn logc steps

corrections to finite size scaling in two dimensional potts models abstract high resolution monte carlo simulations are used to examine the finite size behavior of q state potts models in two dimensions for q 3 we find that at the critical point bulk properties are subject to much larger corrections to finite size scaling than were previously realized for q 4 we find that corrections to finite size scaling are subtle and that the multiplicative logarithmic correction is insufficient to correct the dominant terms

subharmonic oscillations of forced pendulum type equations where f is periodic with minimal period t and mean value zero we have in mind as a particular case the pendulum equation where g x a sin x first results on the existence of subharmonic orbits in a neighborhood of a given periodic motion were obtained by birkhoff and lewis cf 3 and 143 by perturbation type techniques rabinowitz 151 was able to prove the existence of subharmonic solutions for hamiltonian systems by the use of variational methods his approach is not of local type like the one in 3 and enables one to obtain a sequence of solutions whose minimal period tends toward infinity in the case when the hamiltonian function has subquadratic or superquadratic growth these results have been extended in various directions cf 2 5 6 8 13 16 181 local results on subharmonies for the forced pendulum equation can be found in 19 hamiltonian systems with periodic nonlinearity were studied by conley and zehnder 6 they proved the existence of subharmonic solutions under some assumptions on the nondegenerateness of the solutions by the use of morse conley theory in this paper we will prove the existence of subharmonic oscillations of a pendulum type equation by the use of classical morse theory together with an iteration formula for the index due to bott 4 and developed in 7 and l

conformal spectrum of the six vertex model by way of a generalization of analytical methods recently introduced the conformal spectrum of the six vertex model with twisted boundary conditions is analysed nonlinear integral equations are derived from which all scaling dimensions and the spins can be extracted analytically in terms of rogers dilogarithms the scaling dimensions of low lying excitations are given by the so called gaussian dimensions

normal boundary intersection a new method for generating the pareto surface in nonlinear multicriteria optimization problems this paper proposes an alternate method for finding several pareto optimal points for a general nonlinear multicriteria optimization problem such points collectively capture the trade off among the various conflicting objectives it is proved that this method is independent of the relative scales of the functions and is successful in producing an evenly distributed set of points in the pareto set given an evenly distributed set of parameters a property which the popular method of minimizing weighted combinations of objective functions lacks further this method can handle more than two objectives while retaining the computational efficiency of continuation type algorithms this is an improvement over continuation techniques for tracing the trade off curve since continuation strategies cannot easily be extended to handle more than two objectives

conformal anomaly and critical exponents of the spin 1 takhtajan babujian model the authors consider the critical behaviour of the spin 1 hamiltonian of the takhtajan babujian model the bethe ansatz equations for this antiferromagnet in a finite chain are investigated analytically and numerically the conformal anomaly and critical exponents are obtained by exploiting their relations with the eigenspectrum of the finite system the results strongly support the conjecture that the wess zumino witten non linear sigma model with topological charge k 2 is the underlying field theory for this statistical mechanics model

on the rate of convergence in wasserstein distance of the empirical measure let mu n be the empirical measure associated to a n sample of a given probability distribution mu on mathbb r d we are interested in the rate of convergence of mu n to mu when measured in the wasserstein distance of order p 0 we provide some satisfying non asymptotic l p bounds and concentration inequalities for any values of p 0 and d ge 1 we extend also the non asymptotic l p bounds to stationary rho mixing sequences markov chains and to some interacting particle systems

non autonomous second order hamiltonian systems abstract we study the existence of periodic solutions for a second order non autonomous dynamical system containing variable kinetic energy terms our assumptions balance the interaction between the kinetic energy and the potential energy with neither one dominating the other we study sublinear problems and the existence of non constant solutions

existence of infinitely many periodic solutions for ordinary p laplacian systems abstract in this paper we study the existence and multiplicity of non trivial periodic solutions of ordinary p laplacian systems by using the minimax technique in critical point theory we also give an example to illustrate that the obtained results are new even in the case p 2

periodic solutions of large norm of hamiltonian systems abstract hamiltonian systems of ordinary differential equations are studied the only assumption made on the hamiltonian is appropriately rapid growth at infinity it is proved that for any given period there is an unbounded sequence of periodic solutions of the system having the given period

non abelian gauge theory for quantum heisenberg antiferromagnetic chain a continuum su 2s u 1 gauge theory for a heisenberg antiferromagnet with arbitrary spin s is obtained we show that the level 1 su 2 wzw model with a certain marginally irrelevant perturbation describes the low energy phenomena of the heisenberg model with spin 1 2 the model with spins other than 1 2 can be described in the level 2s su 2 wzw model with a certain relevant perturbation we give a qualitative explanation of the haldane conjecture for heisenberg antiferromagnets

conformal invariance and universality in finite size scaling the universal relation between critical exponents and the amplitude of the correlation length divergence as a function of finite size at the critical point of two dimensional systems is shown to be a consequence of conformal invariance both periodic and free boundary conditions are considered

infinite conservation laws in the one dimensional hubbard model we show that the hamiltonian of the 1d hubbard model commutes with a one parameter family of transfer matrices of a new 2d classical model corresponding to two coupled six vertex models central to this result is a new local algebraic relation a generalization of the infinitesimal startriangle relation

enhanced bisection strategies for the maximin efficiency ratio model abstract the maximin efficiency ratio mer model may be regarded as a new form of data envelopment analysis dea model which is based on the maximum decisional efficiency mde estimation principle the mer model involves a special class of generalized fractional programming problems this paper proposes some improved computational algorithms as alternatives to the original bolzano search and other general purpose algorithms for solving the mer model one of these which may be called a cutting wedges algorithm is similar to the algorithms of the cutting planes type but iteratively modifies coefficients of existing constraints rather than adding new constraints a numerical illustration is presented for the new algorithm a combination of the cutting wedges and the general purpose dinkelbach strategies leads to an enhanced bisection algorithm which improves either the upper or lower bound at all iterations

periodic and subharmonic solutions for a class of superquadratic hamiltonian systems abstract some existence theorems are obtained for periodic and subharmonic solutions of a class of superquadratic hamiltonian systems by the minimax methods in critical point theory specially a local link theorem due to li and willem and the generalized mountain pass theorem respectively

on an instance of the inverse shortest paths problem the inverse shortest paths problem in a graph is considered that is the problem of recovering the arc costs given some information about the shortest paths in the graph the problem is first motivated by some practical examples arising from applications an algorithm based on the goldfarb idnani method for convex quadratic programming is then proposed and analyzed for one of the instances of the problem preliminary numerical results are reported

finite size scaling for correlations of quantum spin chains at criticality we study the finite size scaling behavior of two point correlation functions of translationally invariant many body systems at criticality we propose an efficient method for calculating the two point correlation functions in the thermodynamic limit from numerical data of finite systems our method is most effective when applied to a two dimensional classical system which possesses a conformal invariance by using this method with numerical data obtained from exact diagonalizations and monte carlo simulations we study the spin spin correlations of the quantum spin 1 2 and 3 2 antifierromagnetic chains in particular the logarithmic corrections to power law decay of the correlation of the spin 1 2 isotropic heisenberg antiferromagnetic chain are studied thoroughly we clarify the cause of the discrepancy in previous calculations for the logarithmic corrections our result strongly supports the field theoretic prediction based on the mappings to the wess zumino witten nonlinear model or the sine gordon model we also treat logarithmic corrections and crossover phenomena in the spin spin correlation of the spin 3 2 isotropic heisenberg antiferromagnetic chain our results are consistent with the affleck haldane prediction that the correlation of the spin 3 2 chain exhibits a crossover to the same asymptotic behavior as in the spin 1 2 chain

abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity critical point theorems and applications to some nonlinear problems with strong resonance at infinity p bartolo and v benci istituto di matematica applicata via re david x0 bari ital and istituto di analisi matematica palazzo ateneo l ia scolai 2 bari italy received in revised form 20 december 1952

subharmonic solutions of systems of difference equations with periodic perturbations part i existence we consider the existence of subharmonic solutions of systems of difference equations with periodic perturbations the theory of coincidence degree coupled with some detailed a priori estimates is applied to show that the perturbed system admits subharmonic solutions near a hyperbolic periodic orbit of the unperturbed system if the perturbation is sufficiently small

computational difficulties of bilevel linear programming we show using small examples that two algorithms previously published for the bilevel linear programming problem blp may fail to find the optimal solution and thus must be considered to be heuristics a proof is given that solving blp problems is np hard which makes it unlikely that there is a good exact algorithm

the stability of subharmonic solutions for hamiltonian systems abstract in this paper by using the dual morse index theory we study the stability of subharmonic solutions of the non autonomous hamiltonian systems we obtain a infinite sequence of geometrically distinct periodic solutions such that every element has at most one direction of instability i e it has at least 2 n 2 floquet multipliers lying on the unit circle in the complex plane if the periodic solution is non degenerate or it is elliptic all its 2 n floquet multipliers are lying on the unit circle if the periodic solution is degenerate

maximally productive input output units abstract technical or pareto koopmans efficiency models can be based on ratios of weighted sums of outputs to weighted sums of inputs differing meanings have been considered for such factor weights in this paper we use value or cost rate meanings depending on model orientation these meanings permit considering the simultaneous assignment of input and output factor weights along with optimal intensity values for a virtual composite unit constructed from the observed units an optimization principle we call the winners take all criterion is proposed for determining the maximally productive unit s no assumptions are required on the internal transformation processes of the units the model simultaneously determines the intensities and factor weights and results in indefinite quadratic programming problems that simplify to linear programming in certain cases for the general case genetic search is applied numerical illustrations are provided for faculty merit scoring and for the 15 hospital dataset of sherman

test of modular invariance for finite xxz chains the central charge c of the virasoro algebra is determined using its relation to the set of anomalous dimensions of the scaling fields for the critical anisotropic heisenberg chain the results obtained by exactly solving the bethe ansatz for n or 4 are compared with the standard procedure for calculating c in the whole region of anisotropy for odd n the system is no longer modular invariant and the analogous averaging leads to an anisotropy dependent function which has been calculated

inverse optimization for the recovery of constraint parameters abstract most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set we propose two approaches to impute unspecified left hand side constraint coefficients in addition to a cost vector for a given linear optimization problem the first approach identifies parameters minimizing the duality gap while the second minimally perturbs prior estimates of the unspecified parameters to satisfy strong duality if it is possible to satisfy the optimality conditions exactly we apply these two approaches to the general linear optimization problem we also use them to impute unspecified parameters of the uncertainty set for robust linear optimization problems under interval and cardinality constrained uncertainty each inverse optimization model we propose is nonconvex but we show that a globally optimal solution can be obtained either in closed form or by solving a linear number of linear or convex optimization problems

finite size effects and infrared asymptotics of the correlation functions in two dimensions the finite size corrections approach to the calculation of the asymptotics of correlation functions containing the oscillating terms in the asymptotics in 1 1 dimensional theories is presented explicit formulae for the critical exponents in integrable models are obtained

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

subharmonic solutions of sublinear second order systems with impacts abstract we mainly consider subharmonic bouncing solutions of sublinear second order systems with an obstacle based on variational method

a maximum decisional efficiency estimation principle this paper proposes a systematic approach to certain parameter estimation problems relevant to applied optimization models a context specific measure of decision maker performance called decisional efficiency is defined as a function of the unknown parameter vector the values of this measure are considered to be distributed according to a performance density then a principle of maximum decisional efficiency mde is proposed and its relationship to the maximum likelihood principle of statistics is discussed the principle is first illustrated on a problem of group ideal point estimation next estimation of the ratio of ordering and holding costs in inventories managed by the eoq model is considered the results in both these examples are intuitively appealing suggesting face validity of the principle a more detailed illustration is developed for the problem of deriving a consensus scoring model for credit applicants which combines the data of more than one loan officer

large amplitude subharmonic oscillations for scalar second order differential equations with asymmetric nonlinearities abstract we provide sufficient conditions for the existence of subharmonic solutions for equations whose nonlinearity may have a different qualitative behaviour to the right and to the left of the origin the proofs are based on variational methods

subharmonic solutions of second order subquadratic hamiltonian systems with potential changing sign abstract with the aid of some symplectic transformations the existence of subharmonic solutions of the second order hamiltonian system v x t x is considered where the potential v is subquadratic in x as x goes to infinity and can change sign with respect to t

homotopies exploiting newton polytopes for solving sparse polynomial systems this paper is concerned with the problem of finding all isolated solutions of a polynomial system the bkk bound defined as the mixed volume of the newton polytopes of the polynomials in the system is a sharp upper bound for the number of isolated solutions in mathbb c 0 n mathbb c 0 mathbb c backslash 0 of a polynomial system with a sparse monomial structure first an algorithm is described for computing the bkk bound following the lines of bernshtei n s proof the algorithmic construction of the cheater s homotopy or the coefficient homotopy is obtained the mixed homotopy methods can be combined with the random product start systems based on a generalized bezout number applications illustrate the effectiveness of the new approach

statistics with set valued functions applications to inverse approximate optimization much of statistics relies upon four key elements a law of large numbers a calculus to operationalize stochastic convergence a central limit theorem and a framework for constructing local approximations these elements are well understood for objects in a vector space e g points or functions however much statistical theory does not directly translate to sets because they do not form a vector space building on probability theory for random sets this paper uses variational analysis to develop operational tools for statistics with set valued functions these tools are first applied to nonparametric estimation kernel regression of set valued functions the second application is to the problem of inverse approximate optimization in which approximate solutions corrupted by noise to an optimization problem are observed and then used to estimate the amount of suboptimality of the solutions and the parameters of the optimization problem that generated the solutions we show that previous approaches to this problem are statistically inconsistent when the data is corrupted by noise whereas our approach is consistent under mild conditions

genetic search over probability spaces abstract this paper proposes two new crossover operators for searching over discrete probability spaces the design of the operators is considered in the light of recent theoretical insights into genetic search provided by forma analysis a non trivial test problem in enforcing coherency of probability estimates in cross impact analysis highlights the utility of the designed operators the presented operators will be useful for a variety of probability fitting and optimization applications

inverse optimization for linearly constrained convex separable programming problems abstract in this paper we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas for a given feasible point of a convex separable program the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem and when the answer is positive find the parameter values that have the smallest adjustments a sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values inverse optimization formulations are presented with l 1 and l 2 norms these inverse optimization problems are either linear programming when l 1 norm is used in the formulation or convex quadratic separable programming when l 2 norm is used

logarithmic corrections to finite size scaling in strips abstract the corrections to the finite size scaling behaviour of the eigenvalues of the transfer matrix of a critical theory defined on an infinitely long strip of finite width which occur when the hamiltonian contains a marginal operator are computed using conformal invariance they show a calculable universal logarthmic character for the four state potts model they agree with numerical data

periodic solutions for some nonautonomous second order hamiltonian systems the existence and multiplicity of periodic solutions are obtained for nonautonomous second order hamiltonian systems by the minimax methods in critical point theory

a coupled column generation mixed integer approach to optimal planning of intensity modulated radiation therapy for cancer approximately 40 of all u s cancer cases are treated with radiation therapy in intensity modulated radiation therapy imrt the treatment planning problem is to choose external beam angles and their corresponding intensity maps showing how the intensity varies across a given beam to maximize tumor dose subject to the tolerances of surrounding healthy tissues dose like temperature is a quantity defined at each point in the body and the distribution of dose is determined by the choice of treatment parameters available to the planner in addition to absolute dose limits in healthy tissues some tissues have at least one dose volume restriction that requires a fraction of its volume to not exceed a specified tighter threshold level for damage there may also be a homogeneity limit for the tumor that restricts the allowed spread of dose across its volume we formulate this planning problem as a mixed integer program over a coupled pair of column generation processes one designed to produce intensity maps and a second specifying protected area choices for tissues under dose volume restrictions the combined procedure is shown to strike a balance between computing an approximately optimal solution and bounding its maximum possible suboptimality that we believe holds promise for implementations able to offer the power and flexibility of mixed integer linear programming models on instances of practical scale

infinite conformal symmetry of critical fluctuations in two dimensions we study the massless quantum field theories describing the critical points in two dimensional statistical systems these theories are invariant with respect to the infinite dimensional group of conformal analytic transformations it is shown that the local fields forming the operator algebra can be classified according to the irreducible representations of the virasoro algebra exactly solvable theories associated with degenerate representations are analized in these theories the anomalous dimensions are known exactly and the correlation functions satisfy the system of linear differential equations

existence and multiplicity of periodic solutions for a class of second order hamiltonian systems we study the existence and multiplicity of periodic solutions of the following second order hamiltonian system email protected t email protected k t u t w t u t 0 the existence of a nontrivial periodic solution is obtained when w is asymptotically linear at infinity and the existence of infinitely many periodic solutions is also obtained when w is superlinear

performance of some boundary seeking mode estimators on the dome bias model abstract expert estimates can be systematically biased for various reasons the dome perspective bias model provides one instance of this phenomenon given data with this suspected property it is desirable to propose mode estimators which have the capability of producing consensus estimates on the boundary of the convex hull of the sample affine linear models are no doubt the simplest class of functions with that capability this paper uses the maximum decisional efficiency mde principle to estimate the parameters of an affine linear group value function these estimators vary according to the sample aggregator chosen estimators are developed or approximated for the aggregator choices of i mean ii minimum or leontief and iii variance the respective performances of these estimators are assessed and compared on the dome perspective bias model using monte carlo simulation experiments the estimator based on the mean performed uniformly well on a variety of simulated cases however those based on range and variance were not effective

a minimum variance of utility approach to ideal point estimation in certain biased groups abstract this paper discusses a problem of group decision making called ideal point estimation this problem is equivalent to all individuals of the group or a representative committee attempting to estimate the maximum point for an unknown group multiattribute value function the paper concentrates on a type of systematic error which is possible in such processes and proposes a method of estimation the minimum variance of utility method which is capable of debiasing such estimates in certain cases a model of group error called the dome error process is shown to provide a concrete instance of this type of systematic bias the method is illustrated numerically and some applications are discussed

subharmonic solutions with prescribed minimal period for nonautonomous hamiltonian systems on etablit un resultat de multiplicite pour une certaine classe de systemes hamiltoniens periodiques en temps

some np complete problems in quadratic and nonlinear programming in continuous variable smooth nonconvex nonlinear programming we analyze the complexity of checking whether a a given feasible solution is not a local minimum and b the objective function is not bounded below on the set of feasible solutions we construct a special class of indefinite quadratic programs with simple constraints and integer data and show that checking a or b on this class is np complete as a corollary we show that checking whether a given integer square matrix is not copositive is np complete

data driven estimation in equilibrium using inverse optimization equilibrium modeling is common in a variety of fields such as game theory and transportation science the inputs for these models however are often difficult to estimate while their outputs i e the equilibria they are meant to describe are often directly observable by combining ideas from inverse optimization with the theory of variational inequalities we develop an efficient data driven technique for estimating the parameters of these models from observed equilibria we use this technique to estimate the utility functions of players in a game from their observed actions and to estimate the congestion function on a road network from traffic count data a distinguishing feature of our approach is that it supports both parametric and nonparametric estimation by leveraging ideas from statistical learning kernel methods and regularization operators in computational experiments involving nash and wardrop equilibria in a nonparametric setting we find that a we effectively estimate the unknown demand or congestion function respectively and b our proposed regularization technique substantially improves the out of sample performance of our estimators

subharmonics near an equilibrium for some second order hamiltonian systems this work is devoted to the study of subharmonic solutions of a second order hamiltonian system near an equilibrium point say q 0 the problem of existence of periodic solutions from the global point of view is also considered this problem has been studied for the case where the potential is positive and superquadratic in this work a potential v that has change in sign is considered the potential is decomposed as where p is homogeneous superquadratic and nondegenerate and is of higher order near 0 in this paper the existence is shown of a sequence of subharmonic solutions of the equation above that converges to the equilibrium such that their minimal periods converge to infinity this problem is approached from a variational point of view existence of subharmonic and periodic solutions is obtained via minimax techniques

improving the consistency of conditional probability assessments for forecasting and decision making public agencies are very keen on amassing statistics they collect them add them raise them to the nth power take the cube root and prepare wonderful diagrams but what you must never forget is that every one of those figures comes in the first instance from the village watchman who just puts down what he damn pleases sir josiah stamp the assessment of the conditional probabilities of events is useful and needed for forecasting planning and decision making in this paper the difficulties associated with the assessment of these conditional probabilities are examined the necessary and sufficient conditions that the elicited information on conditional probabilities must satisfy are evaluated against actual assessments in several different controlled settings a high frequency of implicit violations of the probability calculus was observed the consistency of the assessments is affected by the causal diagnostic and positive negative relationships of the events use of a judgmental aid in the form of a joint probability table reduces the number of inconsistent responses significantly using the probability axioms it is also shown that only the first order conditional probabilities need be assessed as higher order probabilities are robust to the unconditional and first order conditional assessments

exact correlation amplitude for the heisenberg antiferromagnetic chain the exact amplitude for the asymptotic correlation function in the heisenberg antiferromagnetic chain is determined the behaviour of the correlation functions for small xxz anisotropy and the form of finite size corrections to the correlation function are also analysed

variational elliptic problems which are nonquadratic at infinity p co if n 1 2 then it is well known that the weak solutions u e h 2 of p are the critical points of the c functional j u ulvul dx jcf x u dx where f x s jif x t dt in this variational setting the literature usually distinguishes between two situations for prob lem p the subquadratic situation where the potential f satisfies lim suplsl f x s s2 i c m and the superquadratic situation where f satisfies limlsl m f x s s2 00 the main goal of this paper is to present a unified approach to both situations by means of a condition of nonquadraticity at infinity on f more precisely our hypotheses are as follows

the inverse optimal value problem this paper considers the following inverse optimization problem given a linear program a desired optimal objective value and a set of feasible cost vectors determine a cost vector such that the corresponding optimal objective value of the linear program is closest to the desired value the above problem referred here as the inverse optimal value problem is significantly different from standard inverse optimization problems that involve determining a cost vector for a linear program such that a pre specified solution vector is optimal in this paper we show that the inverse optimal value problem is np hard in general we identify conditions under which the problem reduces to a concave maximization or a concave minimization problem we provide sufficient conditions under which the associated concave minimization problem and correspondingly the inverse optimal value problem is polynomially solvable for the case when the set of feasible cost vectors is polyhedral we describe an algorithm for the inverse optimal value problem based on solving linear and bilinear programming problems some preliminary computational experience is reported

behavioral estimation of mathematical programming objective function coefficients we propose a parameter estimation method based on what we call the minimum decisional regret principle we focus on mathematical programming models with objective functions that depend linearly on costs or other parameters the approach is illustrated for cost estimation in production planning using linear programming models the method uses past planning data to estimate costs that are otherwise difficult to estimate we define a monetary measure of distance between observed plans and optimal ones called decisional regret the proposed estimation algorithm finds parameter values for which the associated optimal plans are as near as possible to the observed ones on average such techniques may be called behavioral estimation because they are based on the observed planning or decision making behavior of managers or firms two numerical illustrations are given a supporting hyperplane algorithm is used to solve the estimation model a method is proposed for obtaining range estimates of the parameters when multiple alternative estimates exist we also propose a new validation approach for this estimation principle which we call the target mode agreement criterion

data driven inverse optimization with imperfect information in data driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal thus the observer seeks the agent s objective function that best explains a historical sequence of signals and corresponding optimal actions we formalize this inverse optimization problem as a distributionally robust program minimizing the worst case risk that the estimated decision i e the decision implied by a particular candidate objective differs from the agent s actual response to a random signal we show that our framework offers attractive out of sample performance guarantees for different prediction errors and that the emerging inverse optimization problems can be reformulated as or approximated by tractable convex programs when the prediction error is measured in the space of objective values a main strength of the proposed approach is that it naturally generalizes to situations where the observer has imperfect information e g when the agent s true objective function is not contained in the space of candidate objectives when the agent suffers from bounded rationality or implementation errors or when the observed signal response pairs are corrupted by measurement noise

notes on periodic solutions of subquadratic second order systems some existence theorems are obtained for periodic solutions of the subquadratic second order systems by the minimax methods in critical point theory

generalized inverse multiobjective optimization with application to cancer therapy we generalize the standard method of solving inverse optimization problems to allow for the solution of inverse problems that would otherwise be ill posed or infeasible in multiobjective linear optimization given a solution that is not a weakly efficient solution to the forward problem our method generates objective function weights that make the given solution a near weakly efficient solution our generalized inverse optimization model specializes to the standard model when the given solution is weakly efficient and retains the complexity of the underlying forward problem we provide a novel interpretation of our inverse formulation as the dual of the well known benson s method and by doing so develop a new connection between inverse optimization and pareto surface approximation techniques we apply our method to prostate cancer data obtained from princess margaret cancer centre in toronto canada we demonstrate that clinically acceptable treatments can be generated using a small number of objective

subharmonic solutions for second order differential systems ink this paper we consider the existence of subharmonic solutions for the problem utt g u t where g rn r is not necessarily convex and r rn is periodic with minimal period t 0

subharmonic solutions for nonautonomous sublinear second order hamiltonian systems some existence theorems are obtained for subharmonic solutions of nonautonomous second order hamiltonian systems by the minimax methods in critical point theory

periodic solutions for a class of nonautonomous subquadratic second order hamiltonian systems some existence theorems are obtained for periodic solutions of a class of unbounded nonautonomous nonconvex subquadratic second order hamiltonian systems by using the minimax methods in critical point theory

periodic and subharmonic solutions of a class of superquadratic hamiltonian systems abstract periodic solutions and infinitely distinct subharmonic solutions are obtained for a class of nonconvex and nonautonomous superquadratic hamiltonian systems z j h z z t by using the minimax methods in critical point theory

a note on dea efficiency assessment using ideal point an improvement of wang and luo s model abstract evaluating the efficiency of organizational units continues to be a difficult problem to solve especially when the multiplicity of inputs resources costs and outputs services products associated with these units is considered this paper considers a previous article published by wang and luo y wang y luo dea efficiency assessment using ideal and anti ideal decision making units applied mathematics and computation 173 2 2006 902 915 in the journal of applied mathematics and computation where data envelopment analysis dea and the technique for order preference by similarity to ideal solution topsis are integrated in ranking of decision making units dmus wang and luo 2006 contribute to a very interesting topic by showing that the topsis idea can be combined to dea for a comprehensive ranking of dmus however this paper finds that their approach is problematic in employing the negative ideal point nip for dea computation their ideal point based models rely on using conflicting efficiency concepts we slightly revised the models so that a dea analysis using topsis idea can be performed numerical demonstration reveals that our approach produces a ranking result that is consistent with that in previous studies

some critical point theorems and their applications to periodic solution for second order hamiltonian systems abstract some critical point theorems without the compactness assumptions are obtained by the reduction method the perturbation argument and the least action principle as applications some existence results of periodic solutions are obtained for nonautonomous second order hamiltonian systems which unify and generalize some recent corresponding results

finite size scaling for the spin heisenberg antiferromagnetic chain corrections to the asymptotic correlation function in a heisenberg spin antiferromagnetic spin chain are known to vanish slowly logarithmically as a function of the distance r or the chain size l this leads to significant differences with numerical results we calculate the sub leading logarithmic corrections to the finite size correlation function using renormalization group improved perturbation theory and compare the result with numerical data

periodic and subharmonic solutions of a class of subquadratic second order hamiltonian systems some solvability conditions of periodic and subharmonic solutions are obtained for a class of subquadratic nonautonomous second order hamiltonian systems by the minimax methods in critical point theory

data driven distributionally robust optimization using the wasserstein metric performance guarantees and tractable reformulations we consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset using the wasserstein metric we construct a ball in the space of multivariate and non discrete probability distributions centered at the uniform distribution on the training samples and we seek decisions that perform best in view of the worst case distribution within this wasserstein ball the state of the art methods for solving the resulting distributionally robust optimization problems rely on global optimization techniques which quickly become computationally excruciating in this paper we demonstrate that under mild assumptions the distributionally robust optimization problems over wasserstein balls can in fact be reformulated as finite convex programs in many interesting cases even as tractable linear programs leveraging recent measure concentration results we also show that their solutions enjoy powerful finite sample performance guarantees our theoretical results are exemplified in mean risk portfolio optimization as well as uncertainty quantification

linear programming system identification we define a version of the inverse linear programming problem that we call linear programming system identification this version of the problem seeks to identify both the objective function coefficient vector and the constraint matrix of a linear programming problem that best fits a set of observed vector pairs one vector is that of actual decisions that we call outputs these are regarded as approximations of optimal decision vectors the other vector consists of the inputs or resources actually used to produce the corresponding outputs we propose an algorithm for approximating the maximum likelihood solution the major limitation of the method is the computation of exact volumes of convex polytopes a numerical illustration is given for simulated data

nonlinear oscillations and boundary value problems for hamiltonian systems we prove the existence of solutions of various boundary value problems for nonautonomous hamiltonian systems with forcing terms begin gathered dot x t h p t x t p t g t hfill dot p t h x t x t p t f t hfill end gathered