Nonlinear rescaling Lagrangians for nonconvex semidefinite programming

Indexed by:期刊论文

Journal:OPTIMIZATION

Included Journals:SCIE

Volume:63

Issue:6,SI

Page Number:899-920

ISSN No.:0233-1934

Key Words:semidefinite programming; nonlinear Lagrangian; augmented Lagrangian; dual algorithm; 90C22; 65K05

Abstract:This paper focuses on the study of rescaling Lagrangians for solving nonconvex semidefinite programming problems. The rescaling nonlinear Lagrangians are generated by Lowner operators associated with convex real-valued functions. A set of conditions on the convex real-valued functions is proposed to guarantee the convergence of nonlinear rescaling Lagrangian algorithms. These conditions are satisfied by well-known nonlinear Lagrangians appeared in the literature. The convergence theorem shows that, under the second-order sufficient conditions with sigma-term and the strict constraint nondegeneracy condition, the nonlinear rescaling Lagrange algorithm is locally convergent when the penalty parameter is less than a threshold and the error bound of solution is proportional to the penalty parameter. Compared to the analysis in the nonlinear rescaling Lagrangian method for nonlinear programming, we have to deal with the sigma term in the convergence analysis.

Date of Publication:2014-06-03