Sequential Quadratic Programming with Penalization of the Displacement

In this paper we study the convergence of a sequential quadratic programming algorithm for, the nonlinear programming problem. The Hessian of the quadratic program is the sum of an approximation of the Lagrangian and of a multiple of the identity that allows us to penalize the displacement. Assuming...

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Bibliographic Details
Published in:SIAM journal on optimization Vol. 5; no. 4; pp. 792 - 812
Main Authors: Bonnans, J. F., Launay, G.
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.11.1995
Subjects:
Algorithms
Approximation
Hypotheses
Lagrange multiplier
Quadratic programming
ISSN:1052-6234, 1095-7189
Online Access:Get full text
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Summary:In this paper we study the convergence of a sequential quadratic programming algorithm for, the nonlinear programming problem. The Hessian of the quadratic program is the sum of an approximation of the Lagrangian and of a multiple of the identity that allows us to penalize the displacement. Assuming only that the direction, is a stationary point of the current quadratic program we study the local convergence properties without strict complementarity. In particular, we use a very weak condition on the approximation of the Hessian to the Lagrangian. We obtain some global and superlinearly convergent algorithm under weak hypotheses. As a particular case we formulate an extension of Newton's method that is quadratically convergent to a point satisfying a strong sufficient second-order condition.
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ISSN:1052-6234
1095-7189
DOI:10.1137/0805038