Sufficient global optimality conditions for weakly convex minimization problems

Authors:
Z. Y. Wu
Affiliations:
Department of Mathematics, Chongqing Normal University, Chongqing, People's Republic of China 400047 and School of Information Technology and Mathematical Sciences, University of Ballarat, Ballara ...
Venue:
Journal of Global Optimization
Year:
2007

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Abstract

In this paper, we present sufficient global optimality conditions for weakly convex minimization problems using abstract convex analysis theory. By introducing (L,X)-subdifferentials of weakly convex functions using a class of quadratic functions, we first obtain some sufficient conditions for global optimization problems with weakly convex objective functions and weakly convex inequality and equality constraints. Some sufficient optimality conditions for problems with additional box constraints and bivalent constraints are then derived.