Large-Scale Nonlinear Constrained Optimization

Conn, Andrew R.; Gould, Nicholas I. M.; Toint, Philippe L.

doi:10.1007/978-94-015-8196-7_3

Cited by 9 publications

(5 citation statements)

References 92 publications

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“…Similarly, substituting forp F in the third block of equations in (5.10), and using the primal-dual equivalence w j = y j gives 10) which are identical to the equations associated with those for the QP subproblem (5.3).…”

Section: Solution Of the Stabilized Sqp Subproblemmentioning

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: Solution Of the Stabilized Sqp Subproblemmentioning

confidence: 99%

A Globally Convergent Stabilized SQP Method

Gill

Robinson

2013

SIAM J. Optim.

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“…The local solution to the problem can be obtained using any local NLP solver. 19 3.2. Simplified Model.…”

Section: Stripping Phasementioning

confidence: 99%

Optimal Groundwater Remediation Network Design Using Selective Membranes

Bringas

Karuppiah

Román

et al. 2007

Ind. Eng. Chem. Res.

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This work deals with the optimal synthesis of groundwater remediation networks for the valorization of anionic pollutants by means of emulsion pertraction technology using hollow fiber modules (HFM). Superstructures that incorporate all possible design alternatives are proposed. The aim of this work is to obtain a minimum cost groundwater remediation network that allows treatment of groundwater to required levels, and also, a contaminant rich solution that can be used for further processing. The optimization of the superstructure is initially formulated as a nonconvex nonlinear programming (NLP) problem. This rigorous NLP model is simplified using some assumptions to get a simplified model which is globally optimized using a Lagrangean decomposition algorithm. This globally optimal solution is used as an initialization point for optimizing the rigorous NLP problem. Three cases involving different numbers of HFM are studied to determine a cost optimized network with an optimal number of modules.

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“…diagonal preconditioners, 2. band preconditioners, 3. incomplete Cholesky preconditioners, 4. expanding band preconditioners, and 5. full-matrix factorization preconditioners. Further details are given in [6].…”

Section: Introductionmentioning

confidence: 99%

Element-by-Element Preconditioners for Large Partially Separable Optimization Problems

Daydé¹,

L’Excellent²,

Gould³

1997

SIAM J. Sci. Comput.

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We study the solution of large-scale nonlinear optimization problems by methods which aim to exploit their inherent structure. In particular, we consider the property of partial separability, first studied by Griewank and Toint [Nonlinear Optimization, 1981, pp. 301-312]. A typical minimization method for nonlinear optimization problems approximately solves a sequence of simplified linearized subproblems. In this paper, we explore how partial separability may be exploited by iterative methods for solving these subproblems. We particularly address the issue of computing effective preconditioners for such iterative methods. We concentrate on element-by-element preconditioners which reflect the structure of the problem. We find that the performance of these methods can be considerably improved by amalgamating elements before applying the preconditioners. We report the results of numerical experiments which demonstrate the effectiveness of this approach.

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Large-Scale Nonlinear Constrained Optimization

Cited by 9 publications

References 92 publications

A Globally Convergent Stabilized SQP Method

A Globally Convergent Stabilized SQP Method

Optimal Groundwater Remediation Network Design Using Selective Membranes

Element-by-Element Preconditioners for Large Partially Separable Optimization Problems

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