Global Optimality Conditions for Some Classes of Optimization Problems

• Published in: Journal of optimization theory and applications Vol. 145; no. 1; pp. 164 - 185
• Main Authors: Wu, Z. Y., Rubinov, A. M.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.04.2010; Springer; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied sciences; Calculus of variations and optimal control; Calculus of Variations and Optimal Control; Optimization; Convex analysis; Engineering; Euclidean space; Exact sciences and technology; Mathematical analysis; Mathematical programming; Mathematics; Mathematics and Statistics; Operational research and scientific management; Operational research. Management science; Operations Research/Decision Theory; Optimization; Sciences and techniques of general use; Studies; Theory of Computation; Optimality conditions; Global optimization; Abstract convexity; Concave function; Abstract convexity; Necessary and sufficient condition; Optimality condition; Global optimum; Optimality criterion; Convex function; Optimization
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-009-9616-2

We establish new necessary and sufficient optimality conditions for global optimization problems. In particular, we establish tractable optimality conditions for the problems of minimizing a weakly convex or concave function subject to standard constraints, such as box constraints, binary constraints, and simplex constraints. We also derive some new necessary and sufficient optimality conditions for quadratic optimization. Our main theoretical tool for establishing these optimality conditions is abstract convexity.