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81.
The main aspect of the paper consists in the application of a particular theorem of separation between two sets to the image
associated with a constrained extremum problem. In the image space, the two sets are a convex cone, which depends on the constraints
(equalities or inequalities) of the given problem, and its image. In this way, a condition for the existence of a regular
saddle point (i.e., a sufficient optimality condition) is obtained. This regularity condition is compared with those existing
in the literature. 相似文献
82.
V. Jeyakumar 《Mathematical Programming》2006,106(1):81-92
The strong conical hull intersection property (CHIP) is a geometric property of a collection of finitely many closed convex
intersecting sets. This basic property, which was introduced by Deutsch et al. in 1997, is one of the central ingredients
in the study of constrained interpolation and best approximation. In this paper we establish that the strong CHIP of intersecting
sets of constraints is the key characterizing property for optimality and strong duality of convex programming problems. We
first show that a sharpened strong CHIP is necessary and sufficient for a complete Lagrange multiplier characterization of
optimality for the convex programming model problem
where C is a closed convex subset of a Banach space X, S is a closed convex cone which does not necessarily have non-empty interior, Y is a Banach space,
is a continuous convex function and g:X→Y is a continuous S-convex function. We also show that the strong CHIP completely characterizes the strong duality for partially finite convex
programs, where Y is finite dimensional and g(x)=−Ax+b and S is a polyhedral convex cone. Global sufficient conditions which are strictly weaker than the Slater type conditions are given
for the strong CHIP and for the sharpened strong CHIP.
The author is grateful to the referees for their constructive comments and valuable suggestions which have contributed to
the final preparation of the paper. 相似文献
83.
Beatriz Hernández-Jiménez Rafaela Osuna-Gómez 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(8):2463-2475
For multiobjective problems with inequality-type constraints the necessary conditions for efficient solutions are presented. These conditions are applied when the constraints do not necessarily satisfy any regularity assumptions, and they are based on the concept of 2-regularity introduced by Izmailov. In general, the necessary optimality conditions are not sufficient and the efficient solution set is not the same as the Karush-Kuhn-Tucker points set. So it is necessary to introduce generalized convexity notions. In the multiobjective non-regular case we give the notion of 2-KKT-pseudoinvex-II problems. This new concept of generalized convexity is both necessary and sufficient to guarantee the characterization of all efficient solutions based on the optimality conditions. 相似文献
84.
The set covering problem (SCP) is central in a wide variety of practical applications for which finding good feasible solutions quickly (often in real-time) is crucial. Surrogate constraint normalization is a classical technique used to derive appropriate weights for surrogate constraint relaxations in mathematical programming. This framework remains the core of the most effective constructive heuristics for the solution of the SCP chiefly represented by the widely-used Chvátal method. This paper introduces a number of normalization rules and demonstrates their superiority to the classical Chvátal rule, especially when solving large scale and real-world instances. Directions for new advances on the creation of more elaborate normalization rules for surrogate heuristics are also provided. 相似文献
85.
86.
Asymptotic constraint qualifications and global error bounds for convex inequalities 总被引:2,自引:0,他引:2
Received October 26, 1996 / Revised version received October 1, 1997 Published online October 9, 1998 相似文献
87.
In this paper, we develop effective methods for solving the power-networking problem encountered by the Tulsa Metro Chamber. The primary objective is the maximization of unique contacts made in meetings with multiple rotations of participants. Mixed-integer and constraint-programming models are developed to optimize small- to medium-scale problems, and a heuristic method is developed for large-scale problems representative of the Chamber’s application. Tight bounds on the dual objective are presented. The constraint-programming model developed as phase one for the heuristic yields many new best-known solutions to the related social-golfer problem. The solutions generated for the power-networking problem enables the Chamber of Commerce to plan meeting assignments much more effectively. 相似文献
88.
We consider optimization problems with a disjunctive structure of the feasible set. Using Guignard-type constraint qualifications
for these optimization problems and exploiting some results for the limiting normal cone by Mordukhovich, we derive different
optimality conditions. Furthermore, we specialize these results to mathematical programs with equilibrium constraints. In
particular, we show that a new constraint qualification, weaker than any other constraint qualification used in the literature,
is enough in order to show that a local minimum results in a so-called M-stationary point. Additional assumptions are also
discussed which guarantee that such an M-stationary point is in fact a strongly stationary point.
相似文献
89.
Michael L. Flegel 《Journal of Mathematical Analysis and Applications》2005,310(1):286-302
Mathematical programs with equilibrium constraints are optimization problems which violate most of the standard constraint qualifications. Hence the usual Karush-Kuhn-Tucker conditions cannot be viewed as first order optimality conditions unless relatively strong assumptions are satisfied. This observation has lead to a number of weaker first order conditions, with M-stationarity being the strongest among these weaker conditions. Here we show that M-stationarity is a first order optimality condition under a very weak Abadie-type constraint qualification. Our approach is inspired by the methodology employed by Jane Ye, who proved the same result using results from optimization problems with variational inequality constraints. In the course of our investigation, several concepts are translated to an MPEC setting, yielding in particular a very strong exact penalization result. 相似文献
90.
This paper studies noncompact feasible sets of a semi-infinite optimization problem which are defined by finitely many equality constraints and infinitely many inequality constraints. The main result is the equivalence of the overall validity of the Extended Mangasarian Fromovitz Constraint Qualification with certain (topological) stability conditions. Furthermore, two perturbation theorems being of independent interest are presented.This work was supported by the Deutsche Forschungsgemeinschaft under grant Gu 304/1-2. 相似文献