Daniel P. Robinson – Page 5 – Optimization Online

A SECOND DERIVATIVE SQP METHOD WITH IMPOSED DESCENT

Published: 2008/06/18

Constrained Nonlinear Optimization, Nonlinear Optimization l1-penalty function, nonlinear inequality constraints, nonlinear programming, nonsmooth optimization, sequential quadratic programming

Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be … Read more

A Primal-Dual Augmented Lagrangian

Published: 2008/05/01, Updated: 2008/05/18

Philip E. Gill

Daniel P. Robinson

Constrained Nonlinear Optimization augmented lagrangian method, bound constrained lagrangian methods, linearly constrained lagrangian methods, nonlinear inequality constraints, nonlinear programming, primal-dual algorithms

Nonlinearly constrained optimization problems can be solved by minimizing a sequence of simpler unconstrained or linearly constrained subproblems. In this paper, we discuss the formulation of subproblems in which the objective is a primal-dual generalization of the Hestenes-Powell augmented Lagrangian function. This generalization has the crucial feature that it is minimized with respect to both … Read more