A globally and superlinearly convergent feasible QP-free method for nonlinear programming

In this paper, we propose a QP-free type algorithm which solves the problem of minimizing a smooth function subject to smooth inequality constraints. In contrast with the SQP methods, each iteration this algorithm only needs to solve systems of linear equations which are derived from the equality pa...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 168; no. 1; pp. 519 - 539
Main Author: Zhu, Zhibin
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.09.2005
Elsevier
Subjects:
Calculus of variations and optimal control
Constrained optimization
Exact sciences and technology
Global convergence
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Numerical methods in mathematical programming
Numerical methods in mathematical programming, optimization and calculus of variations
QP-free algorithm
Sciences and techniques of general use
SQP algorithm
Superlinear convergence
System of linear equations
System of linear equations
Superlinear convergence
Global convergence
QP-free algorithm
SQP algorithm
Constrained optimization
Numerical linear algebra
Non linear programming
Convergence
Equation system
Direct method
Numerical analysis
Linear system
QP free algorithm
Matrix inversion
Applied mathematics
Inequality constraint
Smooth function
Optimality condition
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:In this paper, we propose a QP-free type algorithm which solves the problem of minimizing a smooth function subject to smooth inequality constraints. In contrast with the SQP methods, each iteration this algorithm only needs to solve systems of linear equations which are derived from the equality part in the KKT first order optimality conditions. It is observed that, if the quasi-Newton direction is zero, we can obtain a direction of descent by dropping a constraint from the active set at the current iterate. A high order modified direction is introduced in order to prevent Maratos effect. Global and superlinear convergence are proven under some suitable conditions.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2004.09.034