Name
Title | ||
|---|---|---|
Semismooth SQP method for equality-constrained optimization problems with an application to the lifted reformulation of mathematical programs with complementarity constraints |
Abstract | ||
|---|---|---|
We consider the sequential quadratic programming (SQP) algorithm applied to equality-constrained optimization problems, where the problem data is differentiable with Lipschitz-continuous first derivatives. For this setting, Dennis-More-type analysis of primal superlinear convergence is presented. Our main motivation is a special modification of SQP tailored to the structure of the lifted reformulation of mathematical programs with complementarity constraints (MPCC). For this problem, we propose a special positive definite modification of the matrices in the generalized Hessian, which is suitable for globalization of SQP based on the penalty function, and at the same time can be expected to satisfy our general Dennis-More-type conditions, thus preserving local superlinear convergence. (Standard quasi-Newton updates in the SQP framework require twice differentiability of the problem data at the solution for superlinear convergence.) Preliminary numerical results comparing a number of quasi-Newton versions of semismooth SQP applied to MPCC are also reported. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1080/10556788.2011.557727 | Optimization Methods and Software |
Keywords | Field | DocType |
semismooth sqp,local superlinear convergence,equality-constrained optimization problem,primal superlinear convergence,quasi-newton version,complementarity constraint,semismooth sqp method,problem data,sqp framework,general dennis-more-type condition,superlinear convergence,dennis-more-type analysis,mathematical program,penalty function,sequential quadratic programming,lipschitz continuity,positive definite,satisfiability,second order | Complementarity (molecular biology),Mathematical optimization,Matrix (mathematics),Positive-definite matrix,Hessian matrix,Differentiable function,Sequential quadratic programming,Optimization problem,Mathematics,Penalty method | Journal |
Volume | Issue | ISSN |
26 | 4-5 | 1055-6788 |
Citations | PageRank | References |
1 | 0.37 | 14 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| A. F. Izmailov | 1 | 238 | 21.76 |
| A. L. Pogosyan | 2 | 13 | 1.37 |
| M. V. Solodov | 3 | 600 | 72.47 |