Characterizations of linear suboptimality for mathematical programs with equilibrium constraints |
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Authors: | B S Mordukhovich |
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Institution: | (1) Department of Mathematics, Wayne State University, Detroit, MI 48202, USA |
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Abstract: | The paper is devoted to the study of a new notion of linear suboptimality in constrained mathematical programming. This concept
is different from conventional notions of solutions to optimization-related problems, while seems to be natural and significant
from the viewpoint of modern variational analysis and applications. In contrast to standard notions, it admits complete characterizations
via appropriate constructions of generalized differentiation in nonconvex settings. In this paper we mainly focus on various
classes of mathematical programs with equilibrium constraints (MPECs), whose principal role has been well recognized in optimization
theory and its applications. Based on robust generalized differential calculus, we derive new results giving pointwise necessary
and sufficient conditions for linear suboptimality in general MPECs and its important specifications involving variational
and quasivariational inequalities, implicit complementarity problems, etc.
Research was partially supported by the National Science Foundation under grant DMS-0304989 and by the Australian Research
Council under grant DP-0451168. |
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Keywords: | Nonsmooth optimization Variational analysis Generalized differentiation Mathematical programs with equilibrium constraints Linear suboptimality |
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