Convexification and existence of a saddle point in a pth-power reformulation for nonconvex constrained optimization

✍ Scribed by D. Li; X.L. Sun

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 369 KB
• Volume: 47
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/s0362-546x(01)00663-0

✦ Synopsis

It is well-known that saddle point criteria is a sufficient optimality condition for constrained optimization problems. Convexity is a basic requirement for the development of duality theory and saddle point optimality. In this paper we show that, under some mild conditions, the local convexity of Lagrangian function and hence the existence of a local saddle point pair can be ensured in an equivalent p-th power reformulation for a general class of nonconvex constrained optimization problems. We further investigate the conditions under which a global saddle point pair can be guaranteed to exist. These results expand considerably the class of optimization problems where a saddle point pair exists, thus enlarging the family of nonconvex problems to which the dual-search methods can be applied.