Stabilized sequential quadratic programming for optimization and a stabilized Newton-type method for variational problems

The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve fast convergence despite possible degeneracy of constraints of optimization problems, when the Lagrange multipliers associated to a solution are not unique. Superlinear convergence...

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Vydáno v:Mathematical programming Ročník 125; číslo 1; s. 47 - 73
Hlavní autoři: Fernández, Damián, Solodov, Mikhail
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer-Verlag 01.09.2010
Springer
Springer Nature B.V
Témata:
Algorithms
Applied sciences
Calculus of variations and optimal control
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Convergence
Errors
Exact sciences and technology
Full Length Paper
Inequality
Lagrange multiplier
Lagrange multipliers
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Operational research and scientific management
Operational research. Management science
Optimization
Optimization algorithms
Quadratic programming
Sciences and techniques of general use
Studies
Theoretical
90C30
65K05
Stabilized sequential quadratic programming
Variational inequality
Newton methods
Superlinear convergence
Error bound
Karush–Kuhn–Tucker system
Degenerate system
Karush-Kuhn-Tucker system
Non linear programming
Quadratic programming
Constrained optimization
Lagrange multiplier
Sequential method
Karush Kuhn Tucker method
Variational calculus
Optimality condition
Optimality criterion
Newton method
Numerical convergence
Mathematical programming
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí:The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve fast convergence despite possible degeneracy of constraints of optimization problems, when the Lagrange multipliers associated to a solution are not unique. Superlinear convergence of sSQP had been previously established under the strong second-order sufficient condition for optimality (without any constraint qualification assumptions). We prove a stronger superlinear convergence result than the above, assuming the usual second-order sufficient condition only. In addition, our analysis is carried out in the more general setting of variational problems, for which we introduce a natural extension of sSQP techniques. In the process, we also obtain a new error bound for Karush–Kuhn–Tucker systems for variational problems that holds under an appropriate second-order condition.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-008-0255-4