Line search filter inexact secant methods for nonlinear equality constrained optimization

Local Convergence of Filter Methods for Equality Constrained Nonlinear Programming

In [10] we discuss general conditions to ensure global convergence of inexact restoration filter algorithms for nonlinear programming. In this paper we show how to avoid the Maratos effect by means of a second order correction. The algorithms are based on feasibility and optimality phases, which can be either independent or not. The optimality phase differs from the original one only when a ful...

An Inexact SQP Method for Equality Constrained Optimization

We present an algorithm for large-scale equality constrained optimization. The method is based on a characterization of inexact sequential quadratic programming (SQP) steps that can ensure global convergence. Inexact SQP methods are needed for large-scale applications for which the iteration matrix cannot be explicitly formed or factored and the arising linear systems must be solved using itera...

An inexact Newton method for nonconvex equality constrained optimization

We present a matrix-free line search algorithm for large-scale equality constrained optimization that allows for inexact step computations. For strictly convex problems, the method reduces to the inexact sequential quadratic programming approach proposed by Byrd et al. [SIAM J. Optim. 19(1) 351–369, 2008]. For nonconvex problems, the methodology developed in this paper allows for the presence o...

Maintaining the positive definiteness of the matrices in reduced secant methods for equality constrained optimization

Sequential equality-constrained optimization for nonlinear programming

A new method is proposed for solving optimization problems with equality constraints and bounds on the variables. In the spirit of Sequential Quadratic Programming and Sequential Linearly-Constrained Programming, the new method approximately solves, at each iteration, an equality-constrained optimization problem. The bound constraints are handled in outer iterations by means of an Augmented Lag...