Local saddle point and a class of convexification methods for nonconvex optimization problems

Authors:
Tao Li;Yanjun Wang;Zhian Liang;Panos M. Pardalos
Affiliations:
Department of Applied Mathematics, Shanghai University of Finance & Economics, Shanghai, P.R. China 200433;Department of Applied Mathematics, Shanghai University of Finance & Economics, Shanghai, P.R. China 200433;Department of Applied Mathematics, Shanghai University of Finance & Economics, Shanghai, P.R. China 200433;Department of Industrial and Systems Engineering, University of Gainesville, Gainesville, USA 32611
Venue:
Journal of Global Optimization
Year:
2007

Citing 3
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Abstract

A class of general transformation methods are proposed to convert a nonconvex optimization problem to another equivalent problem. It is shown that under certain assumptions the existence of a local saddle point or local convexity of the Lagrangian function of the equivalent problem (EP) can be guaranteed. Numerical experiments are given to demonstrate the main results geometrically.