Constrained Nonlinear Optimization – Page 73

A BFGS-IP algorithm for solving strongly convex optimization problems with feasibility enforced by an exact penalty approach

Published: 2001/02/01

Constrained Nonlinear Optimization analytic center, bfgs quasi-newton approximations, constrained optimization, convex optimization, infeasible iterates, interior point methods, line-search, primal-dual algorithms, shift and slack variables, superlinear convergence

This paper introduces and analyses a new algorithm for minimizing a convex function subject to a finite number of convex inequality constraints. It is assumed that the Lagrangian of the problem is strongly convex. The algorithm combines interior point methods for dealing with the inequality constraints and quasi-Newton techniques for accelerating the convergence. Feasibility of … Read more

Constraint Identification and Algorithm Stabilization for Degenerate Nonlinear Programs

Published: 2000/12/19, Updated: 2003/05/29

Stephen Wright

Constrained Nonlinear Optimization active constraint identification, degeneracy, nonlinear programming problems, sequential quadratic programming

In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly active constraints. We show that this information can be used to modify the sequential quadratic programming algorithm so … Read more

Benchmarking Optimization Software with COPS

Published: 2000/11/17

Elizabeth D. Dolan

Jorge Moré

Constrained Nonlinear Optimization, Optimization Software Benchmark benchmarking, large-scale optimization

We describe version 2.0 of the COPS set of nonlinearly constrained optimization problems. We have added new problems, as well as streamlined and improved most of the problems. We also provide a comparison of the LANCELOT, LOQO, MINOS, and SNOPT solvers on these problems. CitationTechnical Report ANL/MCS-246 Mathematics and Computer Science Division Argonne National Laboratory … Read more

Feasibility Control in Nonlinear Optimization

Published: 2000/08/29

Marcelo Marazzi

Jorge Nocedal

Constrained Nonlinear Optimization feasibility control, nonlinear g

We analyze the properties that optimization algorithms must possess in order to prevent convergence to non-stationary points for the merit function. We show that demanding the exact satisfaction of constraint linearizations results in difficulties in a wide range of optimization algorithms. Feasibility control is a mechanism that prevents convergence to spurious solutions by ensuring that … Read more