A merit function method for infinite-dimensional SOCCPs

作者：Chiang, Yungyen; Pan, Shaohua; Chen, Jein Shan^*

来源：Journal of Mathematical Analysis and Applications, 2011, 383(1): 159-178.

DOI：10.1016/j.jmaa.2011.05.019

• Hilbert space
• Complementarity
• Second-order cone
• Merit functions

We introduce the Jordan product associated with the second-order cone K into the real Hilbert space H, and then define a one-parametric class of complementarity functions Phi(t) on H x H with the parameter t is an element of [0,2). We show that the squared norm of Phi(t) with t is an element of (0,2) is a continuously F(rechet)-differentiable merit function. By this, the second-order cone complementarity problem (SOCCP) in H can be converted into an unconstrained smooth minimization problem involving this class of merit functions, and furthermore, under the monotonicity assumption, every stationary point of this minimization problem is shown to be a solution of the SOCCP.

• 出版日期2011-11-1
• 单位中山大学; 华南理工大学