Image Space Analysis for Vector Variational Inequalities with Matrix Inequality Constraints and Applications

J. Li () and N. J. Huang
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J. Li: China West Normal University
N. J. Huang: Sichuan University

Journal of Optimization Theory and Applications, 2010, vol. 145, issue 3, No 4, 459-477

Abstract: Abstract In this paper, vector variational inequalities (VVI) with matrix inequality constraints are investigated by using the image space analysis. Linear separation for VVI with matrix inequality constraints is characterized by using the saddle-point conditions of the Lagrangian function. Lagrangian-type necessary and sufficient optimality conditions for VVI with matrix inequality constraints are derived by utilizing the separation theorem. Gap functions for VVI with matrix inequality constraints and weak sharp minimum property for the solutions set of VVI with matrix inequality constraints are also considered. The results obtained above are applied to investigate the Lagrangian-type necessary and sufficient optimality conditions for vector linear semidefinite programming problems as well as VVI with convex quadratic inequality constraints.

Keywords: Vector variational inequalities; Image space analysis; Matrix inequalities; Necessary and sufficient optimality conditions; Semidefinite programming (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-010-9691-4

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