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Lagrange Multipliers in Nonsmooth Semi-Infinite Optimization Problems

Department of Mathematics, Yunnan University, Kunming 650091, Yunman, People’s Republic of China
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China
xyzheng{at}ynu.edu.cn
mayangxq{at}polyu.edu.hk

Using the variational analysis technique, in terms of the epi-coderivative, we provide Lagrange multiplier rules for a class of semi-infinite optimization problems where all functions are lower semicontinuous or locally Lipschitz.

Key Words: Lagrange multiplier; subdifferential; normal cone; epi-coderivative; Borel measure
History: Received: December 5, 2005; revision received: April 11, 2006;