Hidden Convex Minimization

Authors:
Duan Li;Zhi-You Wu;Heung-Wing Joseph Lee;Xin-Min Yang;Lian-Sheng Zhang
Affiliations:
Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong;Aff2 Aff3;Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong;Aff5 Aff6;Department of Mathematics, Shanghai University, Baoshan, PR China 200436
Venue:
Journal of Global Optimization
Year:
2005

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Abstract

A class of nonconvex minimization problems can be classified as hidden convex minimization problems. A nonconvex minimization problem is called a hidden convex minimization problem if there exists an equivalent transformation such that the equivalent transformation of it is a convex minimization problem. Sufficient conditions that are independent of transformations are derived in this paper for identifying such a class of seemingly nonconvex minimization problems that are equivalent to convex minimization problems. Thus, a global optimality can be achieved for this class of hidden convex optimization problems by using local search methods. The results presented in this paper extend the reach of convex minimization by identifying its equivalent with a nonconvex representation.