A filter SQP algorithm without a feasibility restoration phase

Abstract

In this paper we present a filter sequential quadratic programming (SQP) algorithm for solving constrained optimization problems. This algorithm is based on the modified quadratic programming (QP) subproblem proposed by Burke and Han, and it can avoid the infeasibility of the QP subproblem at each iteration. Compared with other filter SQP algorithms, our algorithm does not require any restoration phase procedure which may spend a large amount of computation. We underline that global convergence is derived without assuming any constraint qualifications. Preliminary numerical results are reported

On optimization strategies for parameter estimation in models governed by partial differential equations

“…For simplicity, let us concentrate on the system (28) and (29). The objective herewith is to find the best parameters k XA , k YA , X k that fit the observations of the extraction curve.…”

“…Eqs. (28) and (29) are considered to be constraints of a finite dimensional optimization problem whose unknowns are X(h, t), Y(h, t) at the grid points and, in addition, the parameters k XA , k YA , X k . In other words, this nonlinear programming problem has the form…”

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“…We have in mind recent sequential quadratic programming methods [16,33] whose implementation details are not consolidated, as well as inexact restoration methods and methods based on filters.…”

Optimality properties of an Augmented Lagrangian method on infeasible problems

“…Rigorously speaking, such problems have no solutions at all and, so, a desirable property of algorithms is to detect infeasibility as soon as possible [11,19,21,22,23,30,31,46,32,39,43,47,48]. However, in many practical situations one is interested in optimizing the function, admitting some level of infeasibility.…”