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First order rejection tests for multiple-objective optimization. (English) Zbl 1301.90082

Summary: Three rejection tests for multi-objective optimization problems based on first order optimality conditions are proposed. These tests can certify that a box does not contain any local minimizer, and thus it can be excluded from the search process. They generalize previously proposed rejection tests in several regards: Their scope include inequality and equality constrained smooth or nonsmooth multiple objective problems. Reported experiments show that they allow quite efficiently removing the cluster effect in mono-objective and multi-objective problems, which is one of the key issues in continuous global deterministic optimization.

MSC:

90C29 Multi-objective and goal programming
90C26 Nonconvex programming, global optimization
90C46 Optimality conditions and duality in mathematical programming
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