共查询到20条相似文献,搜索用时 31 毫秒
1.
Valeriano Antunes de Oliveira 《Journal of Computational and Applied Mathematics》2010,234(3):924-933
In this work continuous-time programming problems of vector optimization are considered. Firstly, a nonconvex generalized Gordan’s transposition theorem is obtained. Then, the relationship with the associated weighting scalar problem is studied and saddle point optimality results are established. A scalar dual problem is introduced and duality theorems are given. No differentiability assumption is imposed. 相似文献
2.
A.R. Nazemi 《Journal of Computational and Applied Mathematics》2011,236(6):1282-1295
This paper presents a new neural network model for solving degenerate quadratic minimax (DQM) problems. On the basis of the saddle point theorem, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle, the equilibrium point of the proposed network is proved to be equivalent to the optimal solution of the DQM problems. It is also shown that the proposed network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original problem. Several illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper. 相似文献
3.
This paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables. The investor's problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset. The corresponding optimal portfolio is derived using semi-infinite programming in a soft framework. The return on each asset and their membership functions are described using historical data. The investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio. This approach is illustrated with a numerical example. 相似文献
4.
Yinyu Ye 《Mathematical Programming》2008,111(1-2):315-348
We present polynomial-time interior-point algorithms for solving the Fisher and Arrow–Debreu competitive market equilibrium
problems with linear utilities and n players. Both of them have the arithmetic operation complexity bound of )) for computing an -equilibrium solution. If the problem data are rational numbers and their bit-length is L, then the bound to generate an exact solution is O(n
4
L) which is in line with the best complexity bound for linear programming of the same dimension and size. This is a significant
improvement over the previously best bound )) for approximating the two problems using other methods. The key ingredient to derive these results is to show that these
problems admit convex optimization formulations, efficient barrier functions and fast rounding techniques. We also present
a continuous path leading to the set of the Arrow–Debreu equilibrium, similar to the central path developed for linear programming
interior-point methods. This path is derived from the weighted logarithmic utility and barrier functions and the Brouwer fixed-point
theorem. The defining equations are bilinear and possess some primal-dual structure for the application of the Newton-based
path-following method.
Dedicated to Clovis Gonzaga on the occassion of his 60th birthday.
This author was supported in part by NSF Grants DMS-0306611 and DMS-0604513. The author would like to thank Curtis Eaves,
Osman Güler, Kamal Jain and Mike Todd for insightful discussions on this subject, especially on their mathematical references
and economic interpretations of the fixed-point model presented in this paper. 相似文献
5.
We consider an inverse problem arising from the semi-definite quadratic programming (SDQP) problem. We represent this problem as a cone-constrained minimization problem and its dual (denoted ISDQD) is a semismoothly differentiable (SC1) convex programming problem with fewer variables than the original one. The Karush–Kuhn–Tucker conditions of the dual problem (ISDQD) can be formulated as a system of semismooth equations which involves the projection onto the cone of positive semi-definite matrices. A smoothing Newton method is given for getting a Karush–Kuhn–Tucker point of ISDQD. The proposed method needs to compute the directional derivative of the smoothing projector at the corresponding point and to solve one linear system per iteration. The quadratic convergence of the smoothing Newton method is proved under a suitable condition. Numerical experiments are reported to show that the smoothing Newton method is very effective for solving this type of inverse quadratic programming problems. 相似文献
6.
In this article we consider the portfolio selection problem of an agent with robust preferences in the sense of Gilboa and Schmeidler [Itzhak Gilboa, David Schmeidler, Maxmin expected utility with non-unique prior, Journal of Mathematical Economics 18 (1989) 141–153] in an incomplete market. Downside risk is constrained by a robust version of utility-based shortfall risk. We derive an explicit representation of the optimal terminal wealth in terms of certain worst case measures which can be characterized as minimizers of a dual problem. This dual problem involves a three-dimensional analogue of f-divergences which generalize the notion of relative entropy. 相似文献
7.
Aparna Mehra 《Journal of Mathematical Analysis and Applications》2002,276(2):815-832
In this paper, we establish a scalarization theorem and a Lagrange multiplier theorem for super efficiency in vector optimization problem involving nearly convexlike set-valued maps. A dual is proposed and duality results are obtained in terms of super efficient solutions. A new type of saddle point, called super saddle point, of an appropriate set-valued Lagrangian map is introduced and is used to characterize super efficiency. 相似文献
8.
C.S. Lalitha 《Journal of Mathematical Analysis and Applications》2009,356(1):168-178
In this paper a general analysis of duality for an extended ε-variational inequality problem based on the notions of ε-convexity and ε-conjugacy is performed. Optimal solutions of both the primal and dual problems are also related to the saddle point of an associated Lagrangian. Gap functions for these problems are proposed. An existence theorem for the extended ε-variational inequality is also established by means of the KKM lemma. 相似文献
9.
On weighted multiway cuts in trees 总被引:1,自引:0,他引:1
A min—max theorem is developed for the multiway cut problem of edge-weighted trees. We present a polynomial time algorithm to construct an optimal dual solution, if edge weights come in unary representation. Applications to biology also require some more complex edge weights. We describe a dynamic programming type algorithm for this more general problem from biology and show that our min—max theorem does not apply to it.Corresponding author.Research of the author was supported by the A. v. Humboldt-Stiftung and the U.S. Office of Naval Research under the contract N-0014-91-J-1385. 相似文献
10.
Maurizio Pratelli 《Mediterranean Journal of Mathematics》2005,2(1):103-112
The object of this short note is the proof of a minimax theorem which does not require compactness conditions and is motivated by a problem of optimal investment; the application to the economic problem is illustrated. 相似文献
11.
The classical Fermat-Weber problem is to minimize the sum of the distances from a point in a plane tok given points in the plane. This problem was generalized by Witzgall ton-dimensional space and to allow for a general norm, not necessarily symmetric; he found a dual for this problem. The authors
generalize this result further by proving a duality theorem which includes as special cases a great variety of choices of
norms in the terms of the Fermat-Weber sum. The theorem is proved by applying a general duality theorem of Rockafellar. As
applications, a dual is found for the multi-facility location problem and a nonlinear dual is obtained for a linear programming
problem with a priori bounds for the variables. When the norms concerned are continuously differentiable, formulas are obtained
for retrieving the solution for each primal problem from the solution of its dual. 相似文献
12.
《Optimization》2012,61(5):709-717
In this paper, we present a general Gordan alternative theorem for presubconvexlike functions in a Hausdorff topological linear space. This is then applied to discuss the saddle point theorem, concave-convex condition and minimax theorem for vector extremum problems. 相似文献
13.
Martin Schechter 《Journal of Mathematical Analysis and Applications》2007,327(2):1143-1154
As formulated by Silva [E.A. de B.e. Silva, Linking theorems and applications to semilinear elliptic problems at resonance, Nonlinear Anal. 16 (1991) 455-477] and Schechter [M. Schechter, A generalization of the saddle point method with applications, Ann. Polon. Math. 57 (3) (1992) 269-281; M. Schechter, New saddle point theorems, in: Generalized Functions and Their Applications, Varanasi, 1991, Plenum, New York, 1993, pp. 213-219], the sandwich theorem has become a very useful tool in finding critical points of functionals leading to solutions of partial differential equations. In the present paper, this theorem is strengthened to apply to more general situations. We present some applications. 相似文献
14.
S. Karamardian 《Journal of Optimization Theory and Applications》1969,4(3):167-181
The main existence and uniqueness theorem of Part 1 is applied to three specific problems, namely, (a) the symmetric, dual, nonlinear programs of Dantzig, Eisenberg, and Cottle, (b) the saddle point problem of a differentiable scalar function over an unbounded product set, and (c) the equilibrium point problem of ann-person game.The author is very grateful to the referee for his many helpful comments on an earlier version of the paper. 相似文献
15.
Robust conjugate duality for convex optimization under uncertainty with application to data classification 总被引:1,自引:0,他引:1
In this paper we present a robust conjugate duality theory for convex programming problems in the face of data uncertainty within the framework of robust optimization, extending the powerful conjugate duality technique. We first establish robust strong duality between an uncertain primal parameterized convex programming model problem and its uncertain conjugate dual by proving strong duality between the deterministic robust counterpart of the primal model and the optimistic counterpart of its dual problem under a regularity condition. This regularity condition is not only sufficient for robust duality but also necessary for it whenever robust duality holds for every linear perturbation of the objective function of the primal model problem. More importantly, we show that robust strong duality always holds for partially finite convex programming problems under scenario data uncertainty and that the optimistic counterpart of the dual is a tractable finite dimensional problem. As an application, we also derive a robust conjugate duality theorem for support vector machines which are a class of important convex optimization models for classifying two labelled data sets. The support vector machine has emerged as a powerful modelling tool for machine learning problems of data classification that arise in many areas of application in information and computer sciences. 相似文献
16.
A. Barbagallo 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(3):1104-1123
An evolutionary model for a multi-sector, multi-instrument financial equilibrium problem, with a general utility function, different prices for assets and liabilities and including the expenses for the management of the financial institutions is presented. In this general case, we give the evolutionary financial equilibrium conditions and prove their equivalence with an evolutionary variational inequality, from which existence results of the financial equilibrium follow. Moreover, making use of new nonlinear analysis results, we develop a Lagrange theory which allows one to study the behaviour of the financial equilibrium by means of the Lagrange multipliers. As a product of this analysis, we prove that for the financial model an equilibrium law together with a liability formula must be fulfilled, from which the reorganization of the existing financial disequilibrium depends. 相似文献
17.
Employing the optimality (necessary and sufficient) conditions of a nondifferentiable minimax programming problem in complex spaces, we formulate a one-parametric dual and a parameter free dual problems. On both dual problems, we establish three duality theorems: weak, strong, and strict converse duality theorem, and prove that there is no duality gap between the two dual problems with respect to the primal problem under some generalized convexities of complex functions in the complex programming problem. 相似文献
18.
In Part I of this work we derived a duality theorem for partially finite convex programs, problems for which the standard Slater condition fails almost invariably. Our result depended on a constraint qualification involving the notion ofquasi relative interior. The derivation of the primal solution from a dual solution depended on the differentiability of the dual objective function: the differentiability of various convex functions in lattices was considered at the end of Part I. In Part II we shall apply our results to a number of more concrete problems, including variants of semi-infinite linear programming,L
1 approximation, constrained approximation and interpolation, spectral estimation, semi-infinite transportation problems and the generalized market area problem of Lowe and Hurter (1976). As in Part I, we shall use lattice notation extensively, but, as we illustrated there, in concrete examples lattice-theoretic ideas can be avoided, if preferred, by direct calculation. 相似文献
19.
Fanky极大极小不等式的进一步推广及对变分不等式的应用 总被引:2,自引:0,他引:2
本文引出广义KKM映象的概念,其包含著名的KKM映象为特例.借助于这一映象,我们给出著名的KKM定理和Fan Ky极大极小不等式以一种新的推广形式.作为应用,我们考虑了变分不等式解的存在性问题.本文结果是引文[1~6]中相应结果的改进和发展. 相似文献
20.
A Nash-based collusive game among a finite set of players is one in which the players coordinate in order for each to gain
higher payoffs than those prescribed by the Nash equilibrium solution. In this paper, we study the optimization problem of
such a collusive game in which the players collectively maximize the Nash bargaining objective subject to a set of incentive
compatibility constraints. We present a smooth reformulation of this optimization problem in terms of a nonlinear complementarity
problem. We establish the convexity of the optimization problem in the case where each player's strategy set is unidimensional.
In the multivariate case, we propose upper and lower bounding procedures for the collusive optimization problem and establish
convergence properties of these procedures. Computational results with these procedures for solving some test problems are
reported.
It is with great honor that we dedicate this paper to Professor Terry Rockafellar on the occasion of his 70th birthday. Our
work provides another example showing how Terry's fundamental contributions to convex and variational analysis have impacted
the computational solution of applied game problems.
This author's research was partially supported by the National Science Foundation under grant ECS-0080577.
This author's research was partially supported by the National Science Foundation under grant CCR-0098013. 相似文献