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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Vydáno v:SIAM journal on optimization Ročník 5; číslo 4; s. 792 - 812
Hlavní autoři: Bonnans, J. F., Launay, G.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.11.1995
Témata:
Algorithms
Approximation
Hypotheses
Lagrange multiplier
Quadratic programming
ISSN:1052-6234, 1095-7189
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1052-6234
1095-7189
DOI:10.1137/0805038