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901.
Tadeusz Antczak 《Journal of Global Optimization》2009,43(1):111-140
This paper represents the second part of a study concerning the so-called G-multiobjective programming. A new approach to duality in differentiable vector optimization problems is presented. The techniques
used are based on the results established in the paper: On G-invex multiobjective programming. Part I. Optimality by T.Antczak. In this work, we use a generalization of convexity, namely G-invexity, to prove new duality results for nonlinear differentiable multiobjective programming problems. For such vector
optimization problems, a number of new vector duality problems is introduced. The so-called G-Mond–Weir, G-Wolfe and G-mixed dual vector problems to the primal one are defined. Furthermore, various so-called G-duality theorems are proved between the considered differentiable multiobjective programming problem and its nonconvex vector
G-dual problems. Some previous duality results for differentiable multiobjective programming problems turn out to be special
cases of the results described in the paper. 相似文献
902.
In this paper, we present second-order optimality conditions for convex composite minimization problems in which the objective function is a composition of a finite-valued or a nonfinite-valued lower semicontinuous convex function and aC
1,1 function. The results provide optimality conditions for composite problems under reduced differentiability requirements.This paper is a revised version of the Departmental Preliminary Report AM92/32, School of Mathematics, University of New South Wales, Kensington, NSW, Australia.Research of this author was supported in part by an Australian Research Council Grant. 相似文献
903.
We study nonsmooth mathematical programs with equilibrium constraints. First we consider a general disjunctive program which
embeds a large class of problems with equilibrium constraints. Then, we establish several constraint qualifications for these
optimization problems. In particular, we generalize the Abadie and Guignard-type constraint qualifications. Subsequently,
we specialize these results to mathematical program with equilibrium constraints. In our investigation, we show that a local
minimum results in a so-called M-stationary point under a very weak constraint qualification.
相似文献
904.
Maximal vectors and multi-objective optimization 总被引:3,自引:0,他引:3
J. G. Lin 《Journal of Optimization Theory and Applications》1976,18(1):41-64
Maximal vector andweak-maximal vector are the two basic notions underlying the various broader definitions (like efficiency, admissibility, vector maximum, noninferiority, Pareto's optimum, etc.) for optimal solutions of multi-objective optimization problems. Moreover, the understanding and characterization of maximal and weak-maximal vectors on the space of index vectors (vectors of values of the multiple objective functions) is fundamental and useful to the understanding and characterization of Pareto-optimal and weak-optimal solutions on the space of solutions.This paper is concerned with various characterizations of maximal and weak-maximal vectors in a general subset of the EuclideanN-space, and with necessary conditions for Pareto-optimal and weak-optimal solutions to a generalN-objective optimization problem having inequality, equality, and open-set constraints on then-space. A geometric method is described; the validity of scalarization by linear combination is studied, and weak conditioning by directional convexity is considered; local properties and a fundamental necessary condition are given. A necessary and sufficient condition for maximal vectors in a simplex or a polyhedral cone is derived. Necessary conditions for Pareto-optimal and weak-optimal solutions are given in terms of Lagrange multipliers, linearly independent gradients, Jacobian and Gramian matrices, and Jacobian determinants.Several advantages in approaching the multi-objective optimization problem in two steps (investigate optimal index vectors on the space of index vectors first, and study optimal solutions on the specific space of solutions next) are demonstrated in this paper.This work was supported by the National Science Foundation under Grant No. GK-32701. 相似文献
905.
906.
Optimality Conditions and Duality for a Class of Nonlinear Fractional Programming Problems 总被引:25,自引:0,他引:25
Liang Z. A. Huang H. X. Pardalos P. M. 《Journal of Optimization Theory and Applications》2001,110(3):611-619
In this paper, we present sufficient optimality conditions and duality results for a class of nonlinear fractional programming problems. Our results are based on the properties of sublinear functionals and generalized convex functions. 相似文献
907.
《Optimization》2012,61(5):603-611
Classical mathematics is usually crisp while most real-life problems are not; therefore, classical mathematics is usually not suitable for dealing with real-life problems. In this article, we present a systematic and focused study of the application of rough sets (Z. Pawlak, Rough sets, In. J. Comput. Informa. Sci. 11 (1982), pp. 341–356.) to a basic area of decision theory, namely ‘mathematical programming’. This new framework concerns mathematical programming in a rough environment and is called ‘rough programming’ (L. Baoding, Theory and Practice of Uncertain Programming, 1st ed., Physica-Verlag, Heidelberg, 2002; E.A. Youness, Characterizing solutions of rough programming problems, Eut. J. Oper. Res. 168 (2006), pp. 1019–1029). It implies the existence of the roughness in any part of the problem as a result of the leakage, uncertainty and vagueness in the available information. We classify rough programming problems into three classes according to the place of the roughness. In rough programming, wherever roughness exists, new concepts like rough feasibility and rough optimality come to the front of our interest. The study of convexity for rough programming problems plays a key role in understanding global optimality in a rough environment. For this, a theoretical framework of convexity in rough programming and conceptualization of the solution is created on the lines of their crisp counterparts. 相似文献
908.
Quanxin Zhu 《Mathematical Methods of Operations Research》2007,66(2):299-313
In this paper, we study the average optimality for continuous-time controlled jump Markov processes in general state and action spaces. The criterion to be minimized is the average expected costs. Both the transition rates and the cost rates are allowed to be unbounded. We propose another set of conditions under which we first establish one average optimality inequality by using the well-known “vanishing discounting factor approach”. Then, when the cost (or reward)
rates are nonnegative (or nonpositive), from the average optimality inequality we prove the existence of an average optimal
stationary policy in all randomized history dependent policies by using the Dynkin formula and the Tauberian theorem. Finally, when the cost (or reward) rates have neither upper nor lower bounds, we also prove the existence of an average optimal policy in all (deterministic) stationary policies by constructing a “new”
cost (or reward) rate.
Research partially supported by the Natural Science Foundation of China (Grant No: 10626021) and the Natural Science Foundation
of Guangdong Province (Grant No: 06300957). 相似文献
909.
We consider optimal control problems governed by semilinear elliptic equations with pointwise constraints on the state variable. The main difference with previous papers is that we consider nonlinear boundary conditions, elliptic operators with discontinuous leading coefficients and unbounded controls. We can deal with problems with integral control constraints and the control may be a coefficient of order zero in the equation. We derive optimality conditions by means of a new Lagrange multiplier theorem in Banach spaces. 相似文献
910.
本文研究了文[1]中提出的较多约束规划的基本问题,在给出问题的较多约束集结构表示的基础上,证明了这类问题的较多约束最优解要满足的Fritz John条件和Kuhn-Tucker条件。 相似文献