A penalty-free method for equality constrained optimization

Chen, Zhongwen; Qiu, Songqiang; Jiao, Yujie

doi:10.3934/jimo.2013.9.391

Cited by 7 publications

(2 citation statements)

References 17 publications

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“…Parameters. The choice of parameters is important to numerical performance of genetic algorithm [8], which is the same in GAHJ. For GAHJ, because of the acceleration operator, generation time and population size can be dramatically reduced.…”

Section: Nonuniform Mutation Operatormentioning

confidence: 99%

A hybrid method combining genetic algorithm and Hooke-Jeeves method for constrained global optimization

Long¹,

Wu²

2014

Journal of Industrial &Amp; Management Optimization

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A new global optimization method combining genetic algorithm and Hooke-Jeeves method to solve a class of constrained optimization problems is studied in this paper. We first introduce the quadratic penalty function method and the exact penalty function method to transform the original constrained optimization problem with general equality and inequality constraints into a sequence of optimization problems only with box constraints. Then, the combination of genetic algorithm and Hooke-Jeeves method is applied to solve the transformed optimization problems. Since Hooke-Jeeves method is good at local search, our proposed method dramatically improves the accuracy and convergence rate of genetic algorithm. In view of the derivative-free of Hooke-Jeeves method, our method only requires information of objective function value which not only can overcome the computational difficulties caused by the ill-condition of the square penalty function, but also can handle the nondifferentiability by the exact penalty function. Some well-known test problems are investigated. The numerical results show that our proposed method is efficient and robust.

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Section: Nonuniform Mutation Operatormentioning

confidence: 99%

A hybrid method combining genetic algorithm and Hooke-Jeeves method for constrained global optimization

Long¹,

Wu²

2014

Journal of Industrial &Amp; Management Optimization

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“…In order to handle the selection of the penalty parameter, some researchers present the various techniques without the penalty function, which are called the penalty-free-type methods, for example, see [7,8,11,14,18,19] and the references therein. Some other people research the updating strategies of the penalty parameter adaptively, e.g., [1,4,5,6,9,12,13,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

A line search exact penalty method with bi-object strategy for nonlinear constrained optimization

Chen

Dai

2016

Journal of Computational and Applied Mathematics

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The exact penalty methods are very popular because of their ability to handle degenerate problems and inconsistent constraint linearizations. This paper presentes a line search exact penalty method with bi-object strategy (LSBO) for nonlinear constrained optimization. In the algorithm LSBO, the penalty parameter is selected at every iteration such that the sufficient progress toward feasibility and optimality is guaranteed along the search direction. In contrast with classical exact penalization approaches, LSBO method has two goals to determine whether the current iteration is successful or not. One is improving the feasibility and the other is reducing the value of the objective function. Moreover, the penalty parameter is only related to the information at the current iterate point. The sequence of the penalty parameter is non-monotone, which does not affect the global convergence in theory and is seen to be advantageous in practice. It is shown that the algorithm enjoys favorable global convergence properties under the weaker assumptions. Numerical experiments illustrate the behavior of the algorithm on various difficult situations.

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On the Global Convergence of a Projective Trust Region Algorithm for Nonlinear Equality Constrained Optimization

Pei

Zhu

2018

Acta. Math. Sin.-English Ser.

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A penalty-free method for equality constrained optimization

Cited by 7 publications

References 17 publications

A hybrid method combining genetic algorithm and Hooke-Jeeves method for constrained global optimization

A hybrid method combining genetic algorithm and Hooke-Jeeves method for constrained global optimization

A line search exact penalty method with bi-object strategy for nonlinear constrained optimization

On the Global Convergence of a Projective Trust Region Algorithm for Nonlinear Equality Constrained Optimization

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