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Sufficient conditions for global optimality of semidefinite optimization. (English) Zbl 1278.90302

Summary: By using the Lagrangian function, we investigate the sufficient global optimality conditions for a class of semi-definite optimization problems, where the objective function is general nonlinear, the variables are mixed integers subject to linear matrix inequalities (LMIs) constraints as well as bounded constraints. In addition, the sufficient global optimality conditions for general nonlinear programming problems are derived, where the variables satisfy LMIs constraints and box constraints or bivalent constraints. Furthermore, we give the sufficient global optimality conditions for the standard semi-definite programming problem, where the objective function is linear, the variables satisfy linear inequalities constraints and box constraints.

MSC:

90C22 Semidefinite programming
90C11 Mixed integer programming
90C26 Nonconvex programming, global optimization
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References:

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