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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Vydané v:Journal of optimization theory and applications Ročník 125; číslo 3; s. 497 - 521
Hlavní autori: Akrotirianakis, I., Rustem, B.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York, NY Springer 01.06.2005
Springer Nature B.V
Predmet:
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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Abstract 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.
AbstractList 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.
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. [PUBLICATION ABSTRACT]
Author Rustem, B.
Akrotirianakis, I.
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CitedBy_id crossref_primary_10_1016_j_cor_2023_106236
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Cites_doi 10.1007/BF00939251
10.1007/BF02275347
10.1080/10556780008805791
10.1007/978-3-642-48320-2
10.1137/S1052623496305560
10.1007/BF00939376
10.1023/A:1019284715657
10.1007/BFb0120945
10.1007/BFb0067703
10.1080/10556780108805829
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Springer Science+Business Media, Inc. 2005
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Issue 3
Keywords 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
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Snippet This paper presents a primal-dual interior-point algorithm for solving general constrained nonlinear programming problems. The inequality constraints are...
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SubjectTerms 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
Title Globally Convergent Interior-Point Algorithm for Nonlinear Programming
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