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

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 constraint...