Sufficient conditions for global optimality of semidefinite optimization

* Correspondence: [email protected] Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China Full list of author information is available at the end of the article Abstract In this article, by using the Lagrangian function, we investigate the sufficient global optimality conditions for a class of semi-definite optimization problems, where the objective function are 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 standard semi-definite programming problem, where the objective function is linear, the variables satisfy linear inequalities constraints and box constraints. Mathematics Subject Classification 2010: 90C30; 90C26; 90C11.