constrained optimization – Page 7

Constrained optimization in seismic reflection tomography: an SQP augmented Lagrangian approach

Published: 2004/07/07

Applications - Science and Engineering, Constrained Nonlinear Optimization, Quadratic Programming a priori information, augmented lagrangian method, constrained optimization, least-squares approach, ray tracing, seismic reflection tomography, sequential quadratic programming

Seismic reflection tomography is a method for determining a subsurface velocity model from the traveltimes of seismic waves reflecting on geological interfaces. From an optimization viewpoint, the problem consists in minimizing a nonlinear least-squares function measuring the mismatch between observed traveltimes and those calculated by ray tracing in this model. The introduction of a priori … Read more

A limited memory algorithm for inequality constrained minimization

Published: 2003/10/07

Paul Armand

Philippe Segalat

Constrained Nonlinear Optimization, Nonlinear Optimization constrained optimization, interior point methods, large-scale optimization, limited memory method, quasi-newton methods

A method for solving inequality constrained minimization problems is described. The algorithm is based on a primal-dual interior point approach, with a line search globalization strategy. A quasi-Newton technique (BFGS) with limited memory storage is used to approximate the second derivatives of the functions. The method is especially intended for solving problems with a large … Read more

A hybrid algorithm for nonlinear equality constrained optimization problems: global and local convergence theory

Published: 2003/04/03, Updated: 2014/04/29

Mohammedi El Hallabi

Constrained Nonlinear Optimization, Nonlinear Optimization, Robust Optimization cauchy decrease, constrained optimization, equality constrained, global convergence, negative curvature, non regularity, quadratic convergence, trust-region methods

In this paper we combine both trust-region and linesearch globalization strategies in a globally convergent hybrid algorithm to solve a continuously differentiable nonlinear equality constrained minimization problem. First, the trust-region approach is used to determine a descent direction of the augmented Lagrangian chosen as the merit function, and second, linesearch techniques are used to obtain … Read more

A new exact penalty function

Published: 2002/06/19

Waltraud Huyer

Arnold Neumaier

Constrained Nonlinear Optimization, Nonsmooth Optimization augmented lagrangian method, constrained optimization, exact penalty functions, mangasarian--fromovitz condition, nonlinear programming, nonsmooth optimization

For constrained smooth or nonsmooth optimization problems, new continuously differentiable penalty functions are derived. They are proved exact in the sense that under some nondegeneracy assumption, local optimizers of a nonlinear program are precisely the optimizers of the associated penalty function. This is achieved by augmenting the dimension of the program by a variable that … Read more

A Pattern Search Filter Method for Nonlinear Programming without Derivatives

Published: 2001/03/16

Charles Audet

John E. Dennis, Jr.

Constrained Nonlinear Optimization, Nonsmooth Optimization constrained optimization, derivative-free convergence analysis, filter algorithm, nonlinear programming, pattern search algorithm, surrogate-based optimization

This paper presents and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance. Roughly, a filter method accepts a step that either improves the objective function value or the value of some function that measures the constraint violation. The new algorithm does not compute or approximate any derivatives, … Read more

Feasible Interior Methods Using Slacks for Nonlinear Optimization

Published: 2001/02/12

Richard H. Byrd

Richard A. Waltz

Jorge Nocedal

Constrained Nonlinear Optimization barrier method, constrained optimization, feasible method, interior point methods, large-scale optimization, nonlinear programming, primal-dual algorithms, sequential quadratic programming, trust-region methods

A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the … Read more

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

Published: 2001/02/01

Paul Armand

Jean Charles Gilbert

Sophie Jan-Jégou

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