a gradient algorithm for chance constrained nonlinear goal programming abstract decision environments involve high degrees of uncertainty as well as multiple conflicting objectives often sampling information is available as a means of describing uncertainty this description can be utilized in the form of chance constraints goal programming offers a means of considering multiple conflicting objectives a nonlinear goal programming algorithm is presented based upon the gradient method utilizing an optimal step length for chance constrained goal programming models the resulting algorithm requires assumptions of convex solution sets differentiable and monotonic nonlinear constraints and normally distributed variance of stochastic parameters the algorithm is evaluated for generality reliability and precision sensitivity to parameters and data preparational and computational effort and convergence model sensitivity to parameters is identified as well as appropriate adjustment the algorithm was found to require minimal preparational effort favorable computation time and rapid convergence to optimal solution with the exception of models containing high degrees of nonlinearity

calculus for interval valued functions using generalized hukuhara derivative and applications this paper is devoted to studying differential calculus for interval valued functions by using the generalized hukuhara differentiability which is the most general concept of differentiability for interval valued functions conditions examples and counterexamples for limit continuity integrability and differentiability are given special emphasis is set to the class f t c g t where c is an interval and g is a real function of a real variable here the emphasis is placed on the fact that f and g do not necessarily share their properties underlying the extra care that must be taken into account when dealing with interval valued functions two applications of the obtained results are presented the first one determines a delta method for interval valued random elements in the second application a new procedure to obtain solutions to an interval differential equation is introduced our results are relevant to fuzzy set theory because the usual fuzzy arithmetic extension functions and mathematical analysis are done on a cuts which are intervals

extended karush kuhn tucker condition for constrained interval optimization problems and its application in support vector machines abstract in this paper we correct some errors in the extended first and second gordan s theorems in a recent paper information sciences 504 2019 276 292

k homology asymptotic representations and unsuspended e theory connes and higson defined a bivariant homology theory e a b for separable c algebras the elements of e a b are taken to be homotopy classes of asymptotic momorphisms from sa k to sb k in symbols e a b sa sb k if a is k nuclear then e theory agrees with kasparov s bivariant k theory we show that in many cases one need not take suspensions to calculate the e theory group e a b for many a we show e a b a b k for all b among the a for which this is true are c0 x pt for x with the homotopy type of a finite connected cw complex this gives a concrete realization of k homology related to the brown douglas fillmore description for example k0 x arises as asymptotic representations k0 x c0 x k other a for which our isomorphic holds include the nonunital dimension drop intervals in this case there is no distinction between homomorphisms and asymptotic morphisms so we have succeeded in classifying all homomorphisms from a dimension drop interval to a stable c algebra this was subsequently used by elliott j reine angew math 443 1993 179 219 in the classification of certain c algebras the dimension drop interval may also be used to describe k x z n in terms of paths of asymptotic representations of c0 x

linear programming with a possibilistic objective function abstract this paper proposes some ways for dealing with a linear program when the coefficients of the objective function are subject to possibilistic imprecision i e they are characterized by fuzzy restrictions emphasis is placed upon a passive approach that yields a satisfying solution via an appropriate semi infinite program and an active one that allows to reach a solution with a high possibility level of optimality extensions to the possibilistic constraints case and to the case of multiple objective programming problems with possibilistic coefficients are also hinted we end up with some concluding remarks and indicate axes for further developments

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

fuzzy dea a perceptual evalution method abstract dea data envelopment analysis is a non parametric technique for measuring and evaluating the relative efficiencies of a set of entities with common crisp inputs and outputs in fact in a real evaluation problem input and output data of entities evaluated often fluctuate these fluctuating data can be represented as linguistic variables characterized by fuzzy numbers for reflecting a kind of general feeling or experience of experts based on the fundamental ccr model a fuzzy dea model is proposed to deal with the efficiency evaluation problem with the given fuzzy input and output data furthermore an extension of the fuzzy dea model to a more general form is also proposed with considering the relationship between dea and ra regression analysis using the proposed fuzzy dea models the crisp efficiency in ccr model is extended to be a fuzzy number to reflect the inherent uncertainty in real evaluation problems

on the transient stochastic dynamics driven by gaussian colored noise of systems with time dependent control parameters the effect of initial conditions abstract on a recent work we studied the transient stochastic dynamics driven by gaussian white noise gwn of linear systems with time dependent control parameters by means of the connection between the nonlinear relaxation times nlrt and the quasideterministic qd approach in the present study we make an extension of the analysis to the gaussian colored noise gcn problem here we first calculate the characteristic time associated with the decay of the unstable state of such linear systems when the control parameter is a linear function of time of the form a t bt a0 with b a0 0 which is continuously swept from below to above a threshold t a 0 b this type of linear modulation is known as the ramp model then going further we consider a general case where the control parameter is modulated by a family of functions a t bt a0 with 0 the effects of the coupling between the initial state at time t 0 of the system with the noise are specially emphasized the results of nlrt for the ramp model and the general case are compared

multiple objective linear programming models with interval coefficients an illustrated overview in most real world situations the coefficients of decision support models are not exactly known in this context it is convenient to consider an extension of traditional mathematical programming models incorporating their intrinsic uncertainty without assuming the exactness of the model coefficients interval programming is one of the tools to tackle uncertainty in mathematical programming models moreover most real world problems inherently impose the need to consider multiple conflicting and incommensurate objective functions this paper provides an illustrated overview of the state of the art of interval programming in the context of multiple objective linear programming models

minimax regret solution to linear programming problems with an interval objective function in this paper a linear programming problem with an interval objective function is treated first the previous approaches to this problem are reviewed and the drawbacks are pointed out to improve the drawbacks a new approach to this problem is proposed by introducing the minimax regret criterion as used in decision theory the properties of minimax regret solution are investigated in order to obtain the minimax regret solution a method of solution by a relaxation procedure is proposed it is shown that the solution is obtained by repetitional use of the simplex method a numerical example is given to illustrate the proposed solution method

classifying c algebras via ordered mod p k theory we introduce an order structure on k 0 9 k0 z p this group may also be thought of as ko 7z z p we exhibit new examples of real rank zero c algebras that are inductive limits of finite dimensional and dimension drop algebras have the same ordered graded k theory with order unit and yet are not isomorphic in fact they are not even stably shape equivalent the order structure on k0 z 3 z p naturally distinguishes these algebras the same invariant is used to give an isomorphism theorem for such realrank zero inductive limits as a corollary we obtain an isomorphism theorem for all real rank zero approximately homogeneous c algebras that arise from systems of bounded dimension growth and torsion free k0 group at the 1980 kingston conference effros posed the problem of finding suitable invariants for use in studying c algebras that are limits of sequences of homogeneous c algebras these are now called almost homogeneous ah c algebras the classification of ah algebras is a rapidly developing field and we will not attempt to summarize all this activity instead we will focus on the growth of the invariants used specifically we consider an ah algebra a that is the direct limit o f a system of the form

how to select and how to rank projects the promethee method abstract in this paper we present the promethee methods a new class of outranking methods in multicriteria analysis their main features are simplicity clearness and stability the notion of generalized criterion is used to construct a valued outranking relation all the parameters to be defined have an economic signification so that the decision maker can easily fix them two ways of treatment are proposed it is possible to obtain either a partial preorder promethee i or a complete one promethee ii both on a finite set of feasible actions a comparison is made with the electre iii method the stability of the results given by the two methods is analysed numerical applications are given in order to illustrate the properties of the new methods and some further problems are discussed

violation analysis on two step method for interval linear programming in many real world problems system parameters or model coefficients may be bounded between lower and upper bounds due to a variety of uncertainties over the past decades intensive research efforts have focused on interval linear programming ilp to tackle such uncertainties as one of the most popular methods for solving ilp problems two step method tsm proposed by huang et al in 1995 allows uncertain information to be directly communicated into the optimization process and resulting solutions such that decision alternatives could be generated through the interpretation of interval solutions however part of optimum solution points obtained through tsm may go beyond the decision space in some cases this phenomenon referred to as solution violation may mislead decision makers to unreasonable policies plans or strategies which play important roles in the social and economic development therefore this study first investigates and identifies the essential cause for the solution violation of tsm following that an improved solution method namely itsm is proposed to avoid resulting violation by introducing extra constraints in the solving process a numeric example is then presented to demonstrate the effectiveness of itsm in handling solution violation

wirtinger type integral inequalities for interval valued functions abstract this study presents some wirtinger type integral inequalities for interval valued functions by means of the generalized hukuhara differentiability and the pompeiu hausdorff metric these integral inequalities generalize their respective versions for real valued functions numerical examples that illustrate the applicability of the theory developed herein are also provided

upper and lower approximation models in interval regression using regression quantile techniques in this paper we propose new interval regression analysis based on the regression quantile techniques to analyze a phenomenon in a fuzzy environment we propose two interval approximation models without using all data we first identify the main trend from the designated proportion of the given data to select the main part of data to be analyzed we introduce the regression quantile techniques the obtained model is not influenced by extreme points since it is formulated from the center located main proportion of the given data after that the interval regression model including all data can be identified based on the acquired main trend the obtained interval regression model by the main proportion of the given data is called the lower approximation model while interval regression model by all data is called the upper approximation model for the given phenomenon also it is shown that from the lower approximation model main trend and the upper approximation model we can construct a trapezoidal fuzzy model the membership function of this fuzzy model is useful to obtain the locational information for each observation the characteristic of our approach can be described as obtaining the upper and lower approximation models and combining them to be a fuzzy model for representing the given phenomenon in a fuzzy environment

origins and uses of linear programming methods for treating l1 and l regressions corrections and comments on abstract this note comments on and corrects some of the referrals and comments of castillo et al castillo e minguez r castillo c confino a s 2008 dealing with the multiplicity of solutions of the l 1 and l regression models european journal of operational research 188 460 484 concerning the origins and uses of linear programming to estimate l 1 and l statistical regressions

inductive limits of semiprojective c algebras abstract we prove closure properties for the class of c algebras that are inductive limits of semiprojective c algebras most importantly we show that this class is closed under shape domination and so in particular under shape and homotopy equivalence it follows that the considered class is quite large it contains for instance the stable suspension of any nuclear c algebra satisfying the uct and with torsion free k 0 group in particular the stabilized c algebra of continuous functions on the pointed sphere is isomorphic to an inductive limit of semiprojectives

the karush kuhn tucker optimality conditions in multiobjective programming problems with interval valued objective functions the kkt conditions in multiobjective programming problems with interval valued objective functions are derived in this paper many concepts of pareto optimal solutions are proposed by considering two orderings on the class of all closed intervals in order to consider the differentiation of an interval valued function we invoke the hausdorff metric to define the distance between two closed intervals and the hukuhara difference to define the difference of two closed intervals under these settings we are able to consider the continuity and differentiability of an interval valued function the kkt optimality conditions can then be naturally elicited

constrained regression median for measuring possible salary discrimination abstract this study proposes a new analytical method for empirically examining possible salary discrimination against a protected e g female or minority group the proposed approach is referred to as constrained regression median crm the method can be used for regressing salary with job qualifications as dependent variables the result of crm is transformed into a 2 2 contingency table and the degree of salary discrimination is determined by the result of the contingency table the approach can be easily explained to and understood by lawyers judges and other individuals involved in a discrimination case the crm method is particularly useful and practical when a data set maintains the problems of outlier and or multicollinearity between job qualifications and gender or race

non simple purely infinite c algebras the hausdorff case abstract local and global definitions of pure infiniteness for a c algebra a are compared and equivalence between them is obtained if the primitive ideal space of a is hausdorff and of finite dimension if a has real rank zero or if a is approximately divisible sufficient criteria are given for local pure infiniteness of tensor products they yield that exact simple tensorially non prime c algebras are purely infinite if they have no semi finite lower semi continuous trace one obtains that a is isomorphic to a o if a is 1 purely infinite separable stable nuclear and prim a is a hausdorff space not necessarily of finite dimension

algorithms for linear programming problems with interval objective function coefficients this paper presents three algorithms for solving linear programming problems in which some or all of the objective function coefficients are specified in terms of intervals which algorithm is applicable depends upon a the number of interval objective function coefficients b the number of nonzero objective function coefficients and c whether or not the feasible region is bounded the algorithms output all extreme points and unbounded edge directions that are multiparametrically optimal with respect to the ranges placed on the objective function coefficients the algorithms are most suitable to linear programs in which the objective function coefficients are deterministic but are likely to vary from time period to time period as for example in blending problems

e theory and kk theory for groups which act properly and isometrically on hilbert space a good deal of research in c algebra k theory in recent years has been devoted to the baum connes conjecture 3 which proposes a formula for the k theory of group c algebras that blends group homology with the representation theory of compact subgroups the conjecture has brought c algebra theory into close contact with manifold theory through its obvious similarity to the borel conjecture of surgery theory 9 31 and its links with the theory of positive scalar curvature 27 in addition there are points of contact with harmonic analysis particularly the tempered representation theory of semisimple groups although the proper relation between the baum connes conjecture and representation theory is not well understood the conjecture is most easily formulated for groups which are discrete and torsion free for such a group g there is a natural homomorphism

new efficiency conditions for multiobjective interval valued programming problems abstract in this paper we focus on necessary and sufficient efficiency conditions for optimization problems with multiple objectives and a feasible set defined by interval valued functions a new concept of fritz john and karush kuhn tucker type points is introduced for this mathematical programming problem based on the gh derivative concept the innovation and importance of these concepts are presented from a practical and computational point of view the problem is approached directly without transforming it into a real valued programming problem thereby attaining theoretical results that are more powerful and computationally more efficient under weaker hypotheses we also provide necessary conditions for efficiency which have been inexistent in the relevant literature to date the identification of necessary conditions is important for the development of future computational optimization techniques in an interval valued environment we introduce new generalized convexity notions for gh differentiable interval valued problems which are a generalization of previous concepts and we prove a sufficient efficiency condition based on these concepts finally the efficiency conditions for deterministic programming problems are shown to be particular instances of the results proved in this paper the theoretical developments are illustrated and justified through several numerical examples

fuzzy goal programming a parametric approach narasimhan incorporated fuzzy set theory within goal formulation in 1980 since then much research has been performed in this field and various models for solving fuzzy goal programming have been proposed one of the well known models was proposed by tiwari et al in 1987 19 where an additive model was proposed this paper is an extension to the tiwari et al model that deals with the sum of weighted negative deviations between the desirable achievement degree and the common target here properties of the model are proposed a numerical example is also given to illustrate the approach

multiobjective transportation problem with interval cost source and destination parameters in this paper we focus on the solution procedure of the multiobjective transportation problem motp where the cost coefficients of the objective functions and the source and destination parameters have been expressed as interval values by the decision maker this problem has been transformed into a classical motp where to minimize the interval objective function the order relations that represent the decision maker s preference between interval profits have been defined by the right limit left limit centre and half width of an interval the constraints with interval source and destination parameters have been converted into deterministic ones finally the equivalent transformed problem has been solved by fuzzy programming technique numerical examples have been provided to illustrate the solution procedure for three possible cases of the original problem

stochastic approach versus multiobjective approach for obtaining efficient solutions in stochastic multiobjective programming problems abstract in this work we deal with obtaining efficient solutions for stochastic multiobjective programming problems in general these solutions are obtained in two stages in one of them the stochastic problem is transformed into its equivalent deterministic problem and in the other one some of the existing generating techniques in multiobjective programming are applied to obtain efficient solutions which involves transforming the multiobjective problem into a problem with only one objective function our aim is to determine whether the order in which these two transformations are carried out influences in any way the efficient solution obtained our results show that depending on the type of stochastic criterion followed and the statistical characteristics of the initial problem the order can have an influence on the final set of efficient solutions obtained for a given problem

multivariate formulation of transient stochastic dynamics abstract the objective of this paper is to generalize the formulation reported in previous works which we term as standard formulation of quasideterministic approach to multivariate unstable systems as usual the new formalism is connected with the nonlinear relaxation times to characterize the transient stochastic dynamics of those unstable systems which are governed by a multivariate langevin type equation the generalized method is applied to study two analytical models in two and three variables in order to obtain explicit results and calculate the time scale associated with the decay of the unstable state of such systems the theoretical formalism constitutes an alternative method to study some physical systems in two and three varibles the laser systems represent one possibility in this theoretical context

the best parameter subset using the chebychev curve fitting criterion the chebychev also minimax andl norm criterion has been widely studied as a method for curve fitting published computer codes are available to obtain the optimal parameter estimates to fit a linear function to a set of given points under the chebychev criterion the purpose of this paper is to study procedures for obtaining the best subset ofq parameters from a given set ofm parameters whereq is less than or equal tom

satisfactory solution concepts and their relations for stochastic multiobjective programming problems abstract this work deals with the concept of satisfactory solution for stochastic multiobjective programming smp problems based on previous literature we will introduce different concepts of satisfactory solutions for smp problems define a new concept of solution where the decision maker dm sets his her preferences in terms of two aspiration levels for the stochastic objective and two probabilities to reach those levels and establish some relationship between these concepts the results will aim at featuring these concepts and determine the differences between them moreover the paper proposes a new step by step procedure to exchange information between the analyst and dm prior to solving the problem thus the dm will be able to choose the transformation criterion for each stochastic objective and the aspiration level

goal programming problems with interval coefficients and target intervals abstract in conventional goal programming the coefficients of objective functions and constraints and target values are determined as crisp values however it is not frequent that the coefficients and the target values are known precisely in such cases the coefficients and target values should be represented by intervals reflecting the imprecision this paper treats goal programming problems in which coefficients and target values are given the intervals it is shown that four formulations of the problems can be considered the properties of the four formulated problems are investigated an example is given to demonstrate the differences between the four formulations

an investigation of the use of goal programming to fit response surfaces abstract this paper deals with the development and implementation of goal programming models for fitting response surfaces where the observed data are characterized by certain peculiarities such as the existence of outliers a factorial statistical experiment is designed to compare through multivariate anova various forms of the goal programming algorithm with the traditional ordinary least squares method the comparison is based on both the speed of convergence of the proposed algorithms and the accuracy of the estimated optimum solution relative to the true optimum of a pre specified theoretical response surface results indicate that two different goal programming methods each involving two secondary criteria achieved a more accurate estimated solution than did the ordinary least squares method this advantage is realized at the expense of slower convergence speed however

least squares ridge regression and goal programming constrained regression alternatives abstract ridge regression has been extensively reviewed in the literature of applied statistics as a method for dealing with problems of collinearity in least squares regressions in this paper ordinary least squares and least squares combined with ridge regressions are examined and compared with ordinary goal programming and goal programming combined with constraints on regressand values that admissible statistical estimates must satisfy the comparisons are effected by means of an example in chemical processing that has been extensively treated in the ridge regression literature

fuzzy goal programming with different importance and priorities abstract this paper formulates fuzzy goal programming fgp incorporating different importance and preemptive priorities by using an additive model to maximize the sum of achievement degrees of all fuzzy goals in contrast to previous works the proposed approach allows the decision maker to determine a desirable achievement degree for each fuzzy goal to reflect explicitly the relative importance of these goals this approach can generate a set of achievement degrees consistent with the decision maker s expectations even though the relative importance of the goals may change furthermore in this paper we incorporate the decision maker s preemptive priority structure into a single formulation the resulting solutions satisfy both the preemptive priority structure and have the maximum achievement degrees in sum the proposed approaches effectiveness and computational superiority over the existing approaches are demonstrated and compared with examples from the literature

a study of the dynamical relaxation of unstable states driven by gaussian exponentially correlated noise the coloured noise omstein uhlembeck process problem corresponding to the decay process of unstable states is studied using the nonlinear relaxation time and the quasideterministic approach the effect of the non markovian character in this problem as well as the statistics of the initial conditions are both addressed our general result is applied to the landau model as a typical example

serial correlation estimation through the imprecise goal programming model abstract the goal programming gp model was used as a time series analysis tool that incorporates a serial correlation where the dependent variable is considered as precise this formulation does not take into consideration the decision maker s preferences however the dependent variable can be imprecise and its value can be expressed through an interval the aim of this paper is to develop a new formulation of the gp model for regression with serial correlation where the dependent variable is imprecise the proposed model will also integrate explicitly the decision maker s preferences a numerical example was used to illustrate our model

la k theorie de la c algebre pleine de sl3 c abstract let g be sl 3 c c g c r g the morphism induced by the regular representation and e c g c the trivial representation we prove that e induces a kk equivalence between c g and c r g c we prove this by comparing c g with c g p g where p is a maximal parabolic subgroup in g as a corollary we obtain the computation of k c g

crossed products byc0 x actions abstract suppose thatghas a representation grouph thatgab g g g is compactly generated and thatais ac algebra for which the complete regularization of prim a is a locally compact hausdorff spacex in a previous article we showed that there is a bijection z f between the collection of exterior equivalence classes of locally inner actions g aut a and the collection of principalgab bundlesz together with continuous functionsf x h2 g t in this paper we compute the crossed productsa gin terms of the dataz f andc h

a generalized stochastic goal programming model in this paper we show how one can get stochastic solutions of stochastic multi objective problem smop using goal programming models in literature it is well known that one can reduce a smop to deterministic equivalent problems and reduce the analysis of a stochastic problem to a collection of deterministic problems the first sections of this paper will be devoted to the introduction of deterministic equivalent problems when the feasible set is a random set and we show how to solve them using goal programming technique in the second part we try to go more in depth on notion of smop solution and we suppose that it has to be a random variable we will present stochastic goal programming model for finding stochastic solutions of smop our approach requires more computational time than the one based on deterministic equivalent problems due to the fact that several optimization programs which depend on the number of experiments to be run needed to be solved on the other hand since in our approach we suppose that a smop solution is a random variable according to the central limit theorem the larger will be the sample size and the more precise will be the estimation of the statistical moments of a smop solution the developed model will be illustrated through numerical examples

asymptotically unitary equivalence and asymptotically inner automorphisms let c be a unital ah algebra and let a be a unital separable simple c algebra with tracial rank zero suppose that phi 1 phi 2 colon c to a are two unital monomorphisms we show that there is a continuous path of unitaries u t colon t in 0 infty of a such that lim t to infty u t phi 1 a u t phi 2 a quad hbox rm for all quad a in c if and only if phi 1 phi 2 in kk c a tau circ phi 1 tau circ phi 2 for all tau in t a and the rotation map tilde eta phi 1 phi 2 associated with phi 1 and phi 2 is zero in particular an automorphism alpha on a unital separable simple c algebra a in cal n with tracial rank zero is asymptotically inner if and only if alpha rm id a quad rm in quad kk a a and the rotation map tilde eta phi 1 phi 2 is zero let a be a unital ah algebra not necessarily simple and let alpha in aut a be an automorphism as an application we show that the associated crossed product a rtimes alpha bbb z can be embedded into a unital simple af algebra if and only if a admits a strictly positive alpha invariant tracial state

optimality conditions for fuzzy constrained programming problems abstract this paper solves optimization problems where both the objective and constraints are given by fuzzy functions in order to get it we first prove that these problems are equivalent to optimization problems where the constraints functions are non fuzzy functions and we introduce a new and wider stationary point concept that generalizes all existing concepts so far this new stationary point concept is based on the gh differentiability and has many computational advantages that we describe it is well known that obtain a useful differentiability notion for fuzzy functions is a difficult task without linearity and we are in that case due to the fact that the fuzzy numbers intervals space is a nonlinear one in this direction the gh derivative for fuzzy functions is a concept that is more general than hukuhara and level wise derivatives that are usually used in fuzzy optimization so far in the sense that they can be applied to a wider number of fuzzy function classes than above concepts with this new differentiability concept we prove a necessary optimality condition for fuzzy optimization problems that is more operational and less restrictive that the few ones we can find in the literature so far moreover due to the fact that we do not have a linear space for fuzzy numbers the convex concepts and generalized convex fuzzy function notion are very restrictive also this implies that the sufficiency optimality conditions for fuzzy problems published so far are not useful

fuzzy linear programming problems with fuzzy numbers abstract linear programming problems with fuzzy parameters are formulated by fuzzy functions the ambiguity considered here is not randomness but fuzziness which is associated with the lack of a sharp transition from membership to nonmembership parameters on constraint and objective functions are given by fuzzy numbers in this paper our object is the formulation of a fuzzy linear programming problem to obtain a reasonable solution under consideration of the ambiguity of parameters this fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential

a linearization procedure for quadratic and cubic mixed integer problems several techniques of linearization have appeared in the literature the technique of f glover which seems to be the most efficient linearizes a binary quadratic integer problem of n variables by introducing n new continuous variables and 4n auxiliary linear constraints the new technique proposed in this paper is not only useful in linearizing binary quadratic and cubic integer problems but also applicable to the case of quadratic and to a certain class of cubic mixed integer problems it is shown that the new technique further reduces the number of auxiliary linear constraints from 4n to n while keeping the number of new continuous variables at n for the binary quadratic integer problem of n variables and it requires in the case of a certain class of cubic mixed integer problems having 2n of 0 1 variables only 3n auxiliary linear constraints and the same number of new continuous variables the analytical superiority of the new linearization technique has also been observed in terms of the nu

an efficient linearization approach for mixed integer problems abstract oral and kettani previously developed a linearization technique published in management science in 1990 and in operational research in 1992 for solving quadratic and cubic mixed integer problems for a quadratic problem with n 0 1 variables their method would introduce n additional continuous variables and n auxiliary constraints for a cubic problem with n 0 1 variables their method would introduce 3n additional continuous variables and 3n auxiliary constraints this linearization approach of oral and kettani has been accepted as the most efficient linearization technique published requiring the least number of additional continuous variables and auxiliary constraints however their method is difficult to extend for linearizing higher order polynomial terms that appear in mixed integer problems and in addition all constraints should be kept as linear this note proposes a new general model for linearizing various orders of mixed integer problems which cannot be solved by oral and kettani s model when the order is higher than three some computational results show that the proposed model is more efficient than oral kettani s method because it uses less additional variables and auxiliary constraints to linearize the same size of mixed integer problems in addition the proposed model can be easily applied to polynomial mixed integer terms that appear in the objective function and or constraints

on possibilistic linear programming abstract the problem of processing and combining possibilistic information in the scope of linear programming is approached as apparatus to cope with this problem we use the concepts of more possible value possibly feasible action and possibly efficient action issues regarding the feasibility of the resulting deterministic programs as well as the characterization of their optimal solutions are also discussed

binary interactions and subset choice abstract subset evaluation and choice problems abound in practical decision settings they are often analyzed with linear objective functions that value subsets as sums of utilities of items in the subsets this simplifies assessment and computational tasks but runs a risk of substantial suboptimality because it disregards evaluative interdependencies among items this paper examines a binary interaction model that accounts for preference interdependencies between items ordinal and cardinal versions of the model are axiomatized and compared to the simpler linear model as well as the general model that incorporates all orders of interdependence comparisons of computational complexity for standard subset choice problems are made between the linear and binary interaction models

the dirac operator and the principal series for complex semisimple lie groups the dirac operator plays a fundamental role in the geometric construction of the discrete series for semisimple lie groups we show that at the level of k theory the dirac operator also plays a central role in connection with the principal series for complex connected semisimple lie groups this proves the connes kasparov conjecture for such groups

connective c algebras connectivity is a homotopy invariant property of separable c algebras which has three notable consequences absence of nontrivial projections quasidiagonality and a more geometric realisation of kk theory for nuclear c algebras using asymptotic morphisms the purpose of this paper is to further explore the class of connective c algebras we give new characterisations of connectivity for exact and for nuclear separable c algebras and show that an extension of connective separable nuclear c algebras is connective we establish connectivity or lack of connectivity for c algebras associated to certain classes of groups virtually abelian groups linear connected nilpotent lie groups and linear connected semisimple lie groups

mixed integer programming for the 0 1 maximum probability model abstract in this paper we study the 0 1 maximum probability model that consists in maximizing the probability that a certain quantity ctx is greater than a prescribed constant t where c and x are n vectors c1 cn are mutually independent and normally distributed random variables and x is a vector of n binary variables such that ax b where b is an m vector and a is an m n matrix it is known that this problem can be formulated as a nonlinear fractional program we show how to solve it exactly using mixed integer programming the advantage of the approach is that it requires only standard commercially available software the computational results which we present show that this technique makes it possible to treat instances with up to 100 random variables in a few seconds of cpu time

two stage quadratic integer programs with stochastic right hand sides we consider two stage quadratic integer programs with stochastic right hand sides and present an equivalent reformulation using value functions we propose a two phase solution approach the first phase constructs value functions of quadratic integer programs in both stages the second phase solves the reformulation using a global branch and bound algorithm or a level set approach we derive some basic properties of value functions of quadratic integer programs and utilize them in our algorithms we show that our approach can solve instances whose extensive forms are hundreds of orders of magnitude larger than the largest quadratic integer programming instances solved in the literature

three variable models in multivariate transient stochastic dynamics the presence of constant external force abstract in this work we show that the generalized formalism of the quasideterministic qd approach and its connection with the nonlinear relaxation times nlrt is absolutely consistent with 3 3 matricial models whose elements of matrix are all different from zero in the context of both gaussian white and colored noise in the absence of external force more general results than those reported in 1 2 are given the consistency of the formalism with such models in the presence of constant external force is also verified for gaussian white noise

on the structure of twisted group c algebras we first give general structural results for the twisted group algebras c g of a locally compact group g with large abelian subgroups in particular we use a theorem of williams to realise c g as the sections of a c bundle whose fibres are twisted group algebras of smaller groups and then give criteria for the simplicity of these algebras next we use a device of rosenberg to show that when is a discrete subgroup of a solvable lie group g the k groups k c are isomorphic to certain twisted k groups k g of the homogeneous space g and we discuss how the twisting class h 3 g z depends on the cocycle

a method for solving fuzzy goal programming problems based on minmax approach abstract narasimhan incorporated fuzzy set theory within goal programming formulation in 1980 since then numerous research has been carried out in this field one of the well known models for solving fuzzy goal programming problems was proposed by hannan in 1981 in this paper the conventional minmax approach in goal programming is applied to solve fuzzy goal programming problems it is proved that the proposed model is an extension to hannan model that deals with unbalanced triangular linear membership functions in addition it is shown that the new model is equivalent to a model proposed in 1991 by yang et al moreover a weighted model of the new approach is introduced and is compared with kim and whang s model presented in 1998 a numerical example is given to demonstrate the validity and strengths of the new models

matricial formulation of transient stochastic dynamics driven by gaussian colored noise abstract in physica a 237 1997 113 we have proposed in terms of gaussian white noise gwn a generalized method in terms of eigenfunctions and eigenvalues of the quasideterministic qd approach and its connection with the nonlinear relaxation times nlrt to describe the transient stochastic dynamics of multivariate systems contrary to what happens with the standard formulation of qd approach the generalized theory is focused on those unstable systems which are not necessarily derived from a potential function in the present work we extend the generalized method to the case of gaussian colored noise gcn the coupling between the noise and the initial state of the system as a natural effect in colored noise problem is also addressed to justify the theory we study the same two analytical models in two and three variables of the preceding reference and calculate the time scales associated with those models

an approximate universal coefficient theorem an approximate universal coefficient theorem auct for certain c algebras is established we present a proof that kirchberg phillips s classification theorem for separable nuclear purely infinite simple c algebras is valid for c algebras satisfying the auct instead of the uct it is proved that two versions of auct are in fact the same we also show that c algebras that are locally approximated by c algebras satisfying the auct satisfy the auct as an application we prove that certain simple c algebras which are locally type i are in fact isomorphic to simple ah algebras as another application we show that a sequence of residually finite dimensional c algebras which are asymptotically nuclear and which asymptotically satisfies the auct can be embedded into the same simple af algebra

a projective c algebra related to k theory the c algebra qc is the smallest of the c algebras qa introduced by cuntz j cuntz a new look at kk theory k theory 1 1 1987 31 51 in the context of kk theory an important property of qc is the natural isomorphism k0 a lim qc mn a our main result concerns the exponential boundary map from k0 of a quotient b to k1 of an ideal i we show if a k0 element is realized in hom qc b then its boundary is realized as a unitary in i the picture we obtain of the exponential map is based on a projective c algebra p that is universal for a set relations slightly weaker than the relations that define qc a new shorter proof of the semiprojectivity of qc is described smoothing questions related the relations for qc are addressed

when almost multiplicative morphisms are close to homomorphisms absrract it is shown that approximately multiplicative contractive positive morphisms from c x with dim x 2 into a simple c algebra a of real rank zero and of stable rank one are close to homomorphisms provided that certain k theoretical obstacles vanish as a corollary we show that a homomorphism h c x a is approximated by homomorphisms with finite dimensional range if h gives no k theoretical obstacle

deformations of nilpotent groups and homotopy symmetric c algebras the homotopy symmetric c algebras are those separable c algebras for which one can unsuspend in e theory we find a new simple condition that characterizes homotopy symmetric nuclear c algebras and use it to show that the property of being homotopy symmetric passes to nuclear c subalgebras and it has a number of other significant permanence properties as an application we show that if i g is the kernel of the trivial representation iota c g rightarrow mathbb c for a countable discrete torsion free nilpotent group g then i g is homotopy symmetric and hence the kasparov group kk i g b can be realized as the homotopy classes of asymptotic morphisms i g b otimes mathcal k for any separable c algebra b

letter to the editor an efficient linearization technique for mixed 0 1 polynomial problem this paper addresses a new and efficient linearization technique to solve mixed 0 1 polynomial problems to achieve a global optimal solution given a mixed 0 1 polynomial term z c tx 1x 2 x ny where x 1 x 2 x n are binary 0 1 variables and y is a continuous variable also c t can be either a positive or a negative parameter we transform z into a set of auxiliary constraints which are linear and can be solved by exact methods such as branch and bound algorithms for this purpose we will introduce a method in which the number of additional constraints is decreased significantly rather than the previous methods proposed in the literature as is known in any operations research problem decreasing the number of constraints leads to decreasing the mathematical computations extensively thus research on the reducing number of constraints in mathematical problems in complicated situations have high priority for decision makers in this method each n auxiliary constraints proposed in the last method in the literature for the linearization problem will be replaced by only 3 novel constraints in other words previous methods were dependent on the number of 0 1 variables and therefore one auxiliary constraint was considered per 0 1 variable but this method is completely independent of the number of 0 1 variables and this illustrates the high performance of this method in computation considerations the analysis of this method illustrates the efficiency of the proposed algorithm

generalized interval vector spaces and interval optimization this paper presents a method of endowing the generalized interval space with some different structures such as vector space topological space order relations and algebraic calculus we formulate interval optimization problems and relate them to classic multi objective optimization problems we also present a version of the mini max s theorem in the interval space context this paper presents a method for endowing the generalized interval space with some different structures such as vector spaces order relations and an algebraic calculus with these concepts we formulate interval optimization problems and relate them to classic multi objective optimization problems we also present a version of the von neumann s mini max theorem in the interval context

small sample properties of ml cols and dea estimators of frontier models in the presence of heteroscedasticity by a n bojanic s b caudill and j m ford european journal of operational research 108 1998 140 148 a comment

optimality conditions for generalized differentiable interval valued functions in this paper we study the optimal solutions set for a generalized differentiable interval valued function necessary and sufficient optimality conditions are established for gh differentiable functions convexity assumptions that are necessary or required to ensure the characterization of the optimal solutions are weaker or less strict than those presented in previous works these convexity assumptions are the weakest to characterize the optimal solutions set known results for classical non interval valued optimization are particular cases of the ones proved here