A robust sequential quadratic programming method
type: Item
instance of: scholarly article
title: A robust sequential quadratic programming method
zbMATH Open document ID: 0683.90070
DOI: 10.1007/BF01582294
author: Yanyan Li
published in: Mathematical Programming. Series A. Series B
publication date: 1989-01-01T00:00:00Z
review text: The authors propose a modification of the SQP-approach for solving nonlinear programming problems. It is well-known that in the classical approach developed by Wilson, Han and Powell the quadratic subproblems can be infeasible. To overcome this drawback such QP-subproblems are defined, in which the right-hand vector of the constraints ensures feasibility and furthermore, the search direction obtained from this subproblem is a descent direction for a distance function to measure the nonfeasibility of the actual iteration point. After the discussion of the modified quadratic subproblem special attention is given to the update of the penalty parameter in the merit function which is used in the line search phase for the determination of the step length. Under suitable assumptions it is proved that an SQP-method based on these subproblems will be global convergent to a stationary point, i.e. a point which is either a Kuhn-Tucker point, a Fritz-John point of the nonlinear problem, or a stationary point of the above remarked distance function. At the end of the paper the authors give some useful hints for implementation and two illustrative examples.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 49M30
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 4119949
zbMATH Keywords: sequential quadratic programming
zbMATH Keywords: feasibility ensuring method
zbMATH Keywords: convergence proof
zbMATH Keywords: infeasible
zbMATH Keywords: modified quadratic subproblem
MaRDI profile type: Publication
cites work: Q5684511
cites work: Descent methods for composite nondifferentiable optimization problems
cites work: A Gauss-Newton Approach to Solving Generalized Inequalities
cites work: Projected gradient methods for linearly constrained problems
cites work: A lower bound for the controlling parameters of the exact penalty functions
cites work: Optimization and nonsmooth analysis
cites work: A model algorithm for composite nondifferentiable optimization problems
cites work: Q3928936
cites work: Superlinearly convergent quasi-newton algorithms for nonlinearly constrained optimization problems
cites work: A necessary and sufficient regularity condition to have bounded multipliers in nonconvex programming
cites work: A globally convergent method for nonlinear programming
cites work: Superlinearly convergent variable metric algorithms for general nonlinear programming problems
cites work: Exact penalty functions in nonlinear programming
cites work: On conditions to have bounded multipliers in locally lipschitz programming
cites work: Algorithms for nonlinear constraints that use lagrangian functions
cites work: Q4151662
cites work: Stability Theory for Systems of Inequalities, Part II: Differentiable Nonlinear Systems
cites work: Perturbed Kuhn-Tucker points and rates of convergence for a class of nonlinear-programming algorithms
cites work: The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function. I. Convergence analysis
cites work: Q5603731
cites work: APPROXIMATIVE PROPERTIES OF SETS IN NORMED LINEAR SPACES
description: scientific article; zbMATH DE number 4119949