Globally Convergent Interior-Point Algorithm for Nonlinear Programming

This paper presents a primal-dual interior-point algorithm for solving general constrained nonlinear programming problems. The inequality constraints are incorporated into the objective function by means of a logarithmic barrier function. Also, satisfaction of the equality constraints is enforced th...

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Veröffentlicht in:Journal of optimization theory and applications Jg. 125; H. 3; S. 497 - 521
Hauptverfasser: Akrotirianakis, I., Rustem, B.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY Springer 01.06.2005
Springer Nature B.V
Schlagworte:
Algorithms
Applied sciences
Convergence
Exact sciences and technology
Inequalities
Mathematical analysis
Mathematical models
Mathematical programming
Nonlinear programming
Operational research and scientific management
Operational research. Management science
Optimization
Strategy
Studies
Logarithmic function
Barrier function
Primal-dual interior-point algorithms
Interior point method
Constraint satisfaction
Non linear programming
Adaptive method
merit functions
Penalty function
Inequality constraint
Equality constraint
Primal dual method
convergence theory
Objective function
Quadratic function
ISSN:0022-3239, 1573-2878
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Beschreibung
Zusammenfassung:This paper presents a primal-dual interior-point algorithm for solving general constrained nonlinear programming problems. The inequality constraints are incorporated into the objective function by means of a logarithmic barrier function. Also, satisfaction of the equality constraints is enforced through the use of an adaptive quadratic penalty function. The penalty parameter is determined using a strategy that ensures a descent property for a merit function. Global convergence of the algorithm is achieved through the monotonic decrease of a merit function. Finally, extensive computational results show that the algorithm can solve large and difficult problems in an efficient and robust way.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-005-2086-2