共查询到10条相似文献,搜索用时 78 毫秒
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Numerical Algorithms - In this paper, we investigate two new algorithms for solving bilevel pseudomonotone variational inequality problems in real Hilbert spaces. The advantages of our algorithms... 相似文献
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Parametric global optimisation for bilevel programming 总被引:2,自引:2,他引:0
Nuno P. Faísca Vivek Dua Berç Rustem Pedro M. Saraiva Efstratios N. Pistikopoulos 《Journal of Global Optimization》2007,38(4):609-623
We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based
on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower’s)
problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables
of the outer (leader’s) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem
is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved
to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without
right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global
optimisation strategy. 相似文献
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In this article, we consider bilevel optimization problems with discrete lower level and continuous upper level problems. Taking into account both approaches (optimistic and pessimistic) which have been developed in the literature to deal with this type of problem, we derive some conditions for the existence of solutions. In the case where the lower level is a parametric linear problem, the bilevel problem is transformed into a continuous one. After that, we are able to discuss local optimality conditions using tools of variational analysis for each of the different approaches. Finally, we consider a simple application of our results namely the bilevel programming problem with the minimum spanning tree problem in the lower level. 相似文献
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X. P. Ding 《Journal of Optimization Theory and Applications》2010,146(2):347-357
A new class of bilevel mixed equilibrium problems is introduced and studied in real Banach spaces. By using the auxiliary
principle technique, new iterative algorithms for solving the mixed equilibrium problems and bilevel mixed equilibrium problems
are suggested and analyzed. Strong convergence of the iterative sequences generated by the algorithms is proved under suitable
conditions. The behavior of the solution set of the bilevel mixed equilibrium problem is also discussed. 相似文献
5.
This paper studies the variational inequality problem over a fuzzy domain and variational inequalities for fuzzy mappings over a fuzzy domain. It is shown that such problems can be reduced to bilevel programming problems. A penalty function algorithm is introduced with a convergence proof. Numerical examples are also included to illustrate the solution procedure. 相似文献
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In this paper, we study the existence theorems of systems of variational inclusions problems. As consequences of our results,
we study existence theorems of systems of generalized vector quasi-equilibrium problems, mathematical program with systems
of variational inclusion constraints, bilevel problem with systems of constraints. 相似文献
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Phung M. Duc 《Optimization》2016,65(10):1855-1866
We propose splitting, parallel algorithms for solving strongly equilibrium problems over the intersection of a finite number of closed convex sets given as the fixed-point sets of nonexpansive mappings in real Hilbert spaces. The algorithm is a combination between the gradient method and the Mann-Krasnosel’skii iterative scheme, where the projection can be computed onto each set separately rather than onto their intersection. Strong convergence is proved. Some special cases involving bilevel equilibrium problems with inverse strongly monotone variational inequality, monotone equilibrium constraints and maximal monotone inclusions are discussed. An illustrative example involving a system of integral equations is presented. 相似文献
9.
Tran Viet Anh 《Optimization》2016,65(6):1229-1243
We propose a method for solving bilevel split variational inequalities involving strongly monotone operators in the leader problems and nonexpansive mappings in the follower ones. The proposed method is a combination between the projection method for variational inequality and the Krasnoselskii–Mann scheme for fixed points of nonexpansive mappings. Strong convergence of the iterative process is proved. Special cases are considered. 相似文献
10.
This paper focuses on bilevel programs with a convex lower-level problem violating Slater’s constraint qualification. We relax the constrained domain of the lower-level problem. Then, an approximate solution of the original bilevel program can be obtained by solving this perturbed bilevel program. As the lower-level problem of the perturbed bilevel program satisfies Slater’s constraint qualification, it can be reformulated as a mathematical program with complementarity constraints which can be solved by standard algorithms. The lower convergence properties of the constraint set mapping and the solution set mapping of the lower-level problem of the perturbed bilevel program are expanded. We show that the solutions of a sequence of the perturbed bilevel programs are convergent to that of the original bilevel program under some appropriate conditions. And this convergence result is applied to simple trilevel programs. 相似文献