On the Global Convergence of a Modified Augmented Lagrangian Linesearch Interior-Point Newton Method for Nonlinear Programming

Argaez, Miguel; Tapia, Richard A.

doi:10.1023/a:1015451203254

Cited by 34 publications

(19 citation statements)

References 9 publications

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“…This code is a nonlinear interior point code based on the work in [17,2,3]. The code uses finite difference gradients, either trust region or line search globalization, and a choice of three merit functions.…”

Section: Numerical Resultsmentioning

confidence: 99%

Solution of a Well-Field Design Problem with Implicit Filtering

Kavanagh¹,

Kelley²,

Miller³

et al. 2003

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Abstract. Problems involving the management of groundwater resources occur routinely, and management decisions based upon optimization approaches offer the potential to save substantial amounts of money. However, this class of application is notoriously difficult to solve due to non-convex objective functions with multiple local minima and both nonlinear models and nonlinear constraints. We solve a subset of community test problems from this application field using MODFLOW, a standard groundwater flow model, and IFFCO, an implicit filtering algorithm that was designed to solve problems similar to those of focus in this work. While sampling methods have received only scant attention in the groundwater optimization literature, we show encouraging results that suggest they are deserving of more widespread consideration for this class of problems. In keeping with our objectives for the community problems, we have packaged the approaches used in this work to facilitate additional work on these problems by others and the application of implicit filtering to other problems in this field. We provide the data for our formulation and solution on the web.

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Section: Numerical Resultsmentioning

confidence: 99%

Solution of a Well-Field Design Problem with Implicit Filtering

Kavanagh¹,

Kelley²,

Miller³

et al. 2003

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“…with Lagrange multipliers for the inequalities being defined as y i = µ/c i (x) for i ∈ I. Barrier-SQP methods exploit this interpretation by replacing the general mixed-constraint problem (NP) by a sequence of equality constraint problems in which the inequalities are eliminated using a logarithmic barrier transformation (see, e.g., [2,9,12,14,31,57]). …”

Section: Primal-dual Methodsmentioning

confidence: 99%

“…This equality constrained problem can then be solved using either a line-search or trust-region SQP method. Argaez and Tapia [2] propose a line-search barrier-SQP method in which the merit function includes an augmented Lagrangian term for the equality constraints. Gay, Overton and Wright [31] also use a combined augmented Lagrangian and logarithmic barrier merit function, but propose the use of a modified Cholesky factorization of the condensed Hessian (see Section 1.5) to handle nonconvex problems.…”

Section: Related Workmentioning

confidence: 99%

“…Some merit functions exploit the fact that equations (1.6) are the optimality conditions for the subproblems generated by an SQP method for the problem (1.2). This provides the motivation for many algorithms based on standard line-search or trust-region SQP strategies (see, e.g., [2,9,10,14,31]). These algorithms usually converge to a second-order point, although this can be guaranteed for only some of the methods.…”

Section: Definition Of the Inner Iterationsmentioning

confidence: 99%

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A primal-dual trust region algorithm for nonlinear optimization

Gertz

Gill

2004

Math. Program., Ser. B

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Abstract. This paper concerns general (nonconvex) nonlinear optimization when first and second derivatives of the objective and constraint functions are available. The proposed method is based on finding an approximate solution of a sequence of unconstrained subproblems parameterized by a scalar parameter. The objective function of each unconstrained subproblem is an augmented penalty-barrier function that involves both primal and dual variables. Each subproblem is solved using a second-derivative Newton-type method that employs a combined trust region and line search strategy to ensure global convergence. It is shown that the trustregion step can be computed by factorizing a sequence of systems with diagonally-modified primal-dual structure, where the inertia of these systems can be determined without recourse to a special factorization method. This has the benefit that off-the-shelf linear system software can be used at all times, allowing the straightforward extension to large-scale problems. Numerical results are given for problems in the COPS test collection.

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“…Modern methods, based on interior-point (IP) techniques, sequential quadratic programming (SQP), trust regions, restoration, nonmonotone strategies and advanced sparse linear algebra procedures attracted much more attention [4,5,17,19,21,20,31,32,33,34,46,50,59,62,63,65,66,69].…”

Section: Introductionmentioning

confidence: 99%

Improving ultimate convergence of an augmented Lagrangian method

Birgin

Martínez

2008

Optimization Methods and Software

130

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Optimization methods that employ the classical Powell-Hestenes-Rockafellar Augmented Lagrangian are useful tools for solving Nonlinear Programming problems. Their reputation decreased in the last ten years due to the comparative success of Interior-Point Newtonian algorithms, which are asymptotically faster. In the present research a combination of both approaches is evaluated. The idea is to produce a competitive method, being more robust and efficient than its "pure" counterparts for critical problems. Moreover, an additional hybrid algorithm is defined, in which the Interior Point method is replaced by the Newtonian resolution of a KKT system identified by the Augmented Lagrangian algorithm.

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On the Global Convergence of a Modified Augmented Lagrangian Linesearch Interior-Point Newton Method for Nonlinear Programming

Cited by 34 publications

References 9 publications

Solution of a Well-Field Design Problem with Implicit Filtering

Solution of a Well-Field Design Problem with Implicit Filtering

A primal-dual trust region algorithm for nonlinear optimization

Improving ultimate convergence of an augmented Lagrangian method

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