Active Set Identification in Nonlinear Programming

Oberlin, Christina; Wright, Stephen J.

doi:10.1137/050626776

Cited by 35 publications

(19 citation statements)

References 20 publications

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“…Recently, there has been considerable interest in the formulation of stabilized SQP methods, which are specifically designed to improve the convergence rate for degenerate problems [14,31,35,43,50,51]. Existing stabilized SQP methods are essentially local, in the sense that both the formulation and analysis focus on the properties of the methods in a neighborhood of a solution.…”

Section: Introductionmentioning

confidence: 99%

A Globally Convergent Stabilized SQP Method

Gill

Robinson

2013

SIAM J. Optim.

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Sequential quadratic programming (SQP) methods are a popular class of methods for nonlinearly constrained optimization. They are particularly effective for solving a sequence of related problems, such as those arising in mixedinteger nonlinear programming and the optimization of functions subject to differential equation constraints.Recently, there has been considerable interest in the formulation of stabilized SQP methods, which are specifically designed to handle degenerate optimization problems. Existing stabilized SQP methods are essentially local, in the sense that both the formulation and analysis focus on the properties of the methods in a neighborhood of a solution. A new SQP method is proposed that has favorable global convergence properties yet, under suitable assumptions, is equivalent to a variant of the conventional stabilized SQP method in the neighborhood of a solution. The method combines a primal-dual generalized augmented Lagrangian function with a flexible line search to obtain a sequence of improving estimates of the solution. The method incorporates a convexification algorithm that allows the use of exact second-derivatives to define a convex quadratic programming (QP) subproblem without requiring that the Hessian of the Lagrangian be positive definite in the neighborhood of a solution. This gives the potential for fast convergence in the neighborhood of a solution. Additional benefits of the method are that each QP subproblem is regularized and the QP subproblem always has a known feasible point. Numerical experiments are presented for a subset of the problems from the CUTEr test collection.

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Section: Introductionmentioning

confidence: 99%

A Globally Convergent Stabilized SQP Method

Gill

Robinson

2013

SIAM J. Optim.

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“…This so-called sequential linear-quadratic programming (SL-QP) method has recently received much attention [2,3,8,10,15,21], and numerical experience suggests that it holds promise for large-scale applications.…”

Section: Introductionmentioning

confidence: 99%

On the use of piecewise linear models in nonlinear programming

Byrd

Nocedal²,

Waltz

et al. 2011

Math. Program.

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This paper presents an active-set algorithm for large-scale optimization that occupies the middle ground between sequential quadratic programming (SQP) and sequential linear-quadratic programming (SL-QP) methods. It consists of two phases. The algorithm first minimizes a piecewise linear approximation of the Lagrangian, subject to a linearization of the constraints, to determine a working set. Then, an equality constrained subproblem based on this working set and using second derivative information is solved in order to promote fast convergence. A study of the local and global convergence properties of the algorithm highlights the importance of the placement of the interpolation points that determine the piecewise linear model of the Lagrangian.

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“…In this paper, we propose a new algorithm for the solution of problem (1.1). The new algorithm is based on the accurate active set identification technique proposed in [9], [24]. It generates feasible iterates.…”

Section: Introductionmentioning

confidence: 99%