Sufficient global optimality conditions for weakly convex minimization problems |
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| Authors: | Z Y Wu |
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| Institution: | (1) Department of Mathematics, Chongqing Normal University, Chongqing, 400047, People’s Republic of China;(2) Present address: School of Information Technology and Mathematical Sciences, University of Ballarat, Ballarat, 3353, VIC, Australia |
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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.
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| Keywords: | Global optimization Optimality conditions Weakly convex minimization |
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