A primal-dual interior point method for nonlinear semidefinite programming

作者：Yamashita Hiroshi; Yabe Hiroshi^*; Harada Kouhei

来源：Mathematical Programming, 2012, 135(1-2): 89-121.

DOI：10.1007/s10107-011-0449-z

• Nonlinear semidefinite programming
• Primal-dual interior point method
• Barrier penalty function
• Primal-dual merit function
• Global convergence

This paper is concerned with a primal-dual interior point method for solving nonlinear semidefinite programming problems. The method consists of the outer iteration (SDPIP) that finds a KKT point and the inner iteration (SDPLS) that calculates an approximate barrier KKT point. Algorithm SDPLS uses a commutative class of Newton-like directions for the generation of line search directions. By combining the primal barrier penalty function and the primal-dual barrier function, a new primal-dual merit function is proposed. We prove the global convergence property of our method. Finally some numerical experiments are given.

• 出版日期2012-10