zbMATH — the first resource for mathematics

Mathematical programs with equilibrium constraints: the existence of feasible point. (English) Zbl 1124.90033
Summary: This article studies three classes of optimization problems with bilevel structure including mathematical programs with equilibrium constraints (MPECs) and semi-infinite problems (SIPs). The main goal of this article is to provide results which establish the existence of feasible points of the problems. These results are based on the so-called KKM lemma. We are also interested in the convexity properties of these problems.

90C30 Nonlinear programming
90C34 Semi-infinite programming
49J53 Set-valued and variational analysis
Full Text: DOI
[1] Aubin JP, Differential Inclusion (1994)
[2] Bard JF, Nonconvex Optimization and its Applications 30 (1998)
[3] Birbil S, European Journal of Operational Research 169 pp 1108– (2006) · Zbl 1079.90152 · doi:10.1016/j.ejor.2004.07.075
[4] DOI: 10.1006/jmaa.1996.0376 · Zbl 0883.47067 · doi:10.1006/jmaa.1996.0376
[5] Deguire P, LS-majorized mappings and their applications to minimax and variational inequalities in the product topological spaces.Nonlinear Analysis, Theory Methods and Applications 37 pp 933– (1999)
[6] Luo ZQ, Mathematical Programs with Equilibrium Constraint (1997)
[7] DOI: 10.1016/S0377-0427(00)00548-3 · Zbl 0990.49003 · doi:10.1016/S0377-0427(00)00548-3
[8] Lin LJ, Journal of Optimization Theory and Applications 117 pp 121– (2003) · Zbl 1063.90062 · doi:10.1023/A:1023656507786
[9] Sion M, Pacific Journal of Mathematics 8 pp 171– (1958) · Zbl 0081.11502 · doi:10.2140/pjm.1958.8.171
[10] Stein O, Bilevel Strategies in Semi-infinite Programming (2003) · Zbl 1103.90094 · doi:10.1007/978-1-4419-9164-5
[11] DOI: 10.1016/S0377-2217(01)00307-1 · Zbl 1081.90063 · doi:10.1016/S0377-2217(01)00307-1
[12] Tan NX, Mathematische Nachrichten 122 pp 231– (1985) · doi:10.1002/mana.19851220123
[13] Tarafadar E, Proceedings of the American Mathematical Society 67 pp 95– (1977) · doi:10.1090/S0002-9939-1977-0467408-7
[14] Yuan G.X.-Z., KKM Theory and Applications in Nonlinear Analysis (1999) · Zbl 0936.47034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.