An Exact Potential Method for Constrained Maxima

Pietrzykowski, Tomasz

doi:10.1137/0706028

Cited by 152 publications

(48 citation statements)

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“…For the equality constrained problem, Fletcher [4] has found a continuously differentiable exact penalty function with a single parameter for which a correct parameter choice is not difficult. Similar results have been developed for the inequality constrained nonlinear program by Zangwill [9], Pietrzykowski [8], and Evans et al [2]. In each of these cases, however, the exact penalty functions studied are not continuously differentiable.…”

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confidence: 60%

Iterative determination of parameters for an exact penalty function

Hartman

1975

J Optim Theory Appl

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As an approach to solving nonlinear programs, we study a class of functions known to be exact penalty functions for a proper choice of the parameters. The goal is to iteratively determine the correct parameter values. A basic algorithm has been developed. We have proved that this algorithm converges for concave programs, and in the limited computational tests performed to date it has always converged for nonconcave programs also.Suggestions for continuing the work are given.

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confidence: 60%

Iterative determination of parameters for an exact penalty function

Hartman

1975

J Optim Theory Appl

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“…, s equal to 1, we get the most known nondifferentiable exact penalty function, called the exact l 1 penalty function (also the absolute value penalty function). The exact l 1 penalty function method has been introduced by Pietrzykowski [10]. Most of the literature on nondifferentiable exact penalty function methods for optimization problems is devoted to the study of conditions ensuring that a (local) optimum of the given constrained optimization problem is also an unconstrained (local) minimizer of the exact penalty function.…”

Section: The Exact Minimax Penalty Function Methodsmentioning

confidence: 99%

A Lower Bound for the Penalty Parameter in the Exact Minimax Penalty Function Method for Solving Nondifferentiable Extremum Problems

Antczak

2013

J Optim Theory Appl

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In the paper, we consider the exact minimax penalty function method used for solving a general nondifferentiable extremum problem with both inequality and equality constraints. We analyze the relationship between an optimal solution in the given constrained extremum problem and a minimizer in its associated penalized optimization problem with the exact minimax penalty function under the assumption of convexity of the functions constituting the considered optimization problem (with the exception of those equality constraint functions for which the associated Lagrange multipliers are negative-these functions should be assumed to be concave). The lower bound of the penalty parameter is given such that, for every value of the penalty parameter above the threshold, the equivalence holds between the set of optimal solutions in the given extremum problem and the set of minimizers in its associated penalized optimization problem with the exact minimax penalty function.Keywords Exact minimax penalty function method · Minimax penalized optimization problem · Exactness of the exact minimax penalty function method · Convex function

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“…Exact penalty methods are therefore less dependent on the penalty parameter than the quadratic penalty method for which a sequence of subproblems with a divergent series of penalty parameters must be solved. Use of such a function was proposed by Zangwill [43] and Pietrzykowski [35] and methods using it were proposed by Conn and Pietrzykowski [12,13]. An algorithmic framework that forms the basis for many penalty methods proposed in the literature is as follows.…”

Section: Classical Penalty Frameworkmentioning

confidence: 99%

Steering exact penalty methods for nonlinear programming

Byrd

Nocedal

Waltz

2008

Optimization Methods and Software

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This paper reviews, extends and analyzes a new class of penalty methods for nonlinear optimization. These methods adjust the penalty parameter dynamically; by controlling the degree of linear feasibility achieved at every iteration, they promote balanced progress toward optimality and feasibility. In contrast with classical approaches, the choice of the penalty parameter ceases to be a heuristic and is determined, instead, by a subproblem with clearly defined objectives. The new penalty update strategy is presented in the context of sequential quadratic programming (SQP) and sequential linear-quadratic programming (SLQP) methods that use trust regions to promote convergence. The paper concludes with a discussion of penalty parameters for merit functions used in line search methods.

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An Exact Potential Method for Constrained Maxima

Cited by 152 publications

References 1 publication

Iterative determination of parameters for an exact penalty function

Iterative determination of parameters for an exact penalty function

A Lower Bound for the Penalty Parameter in the Exact Minimax Penalty Function Method for Solving Nondifferentiable Extremum Problems

Steering exact penalty methods for nonlinear programming

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