On the accurate identification of active set for constrained minimax problems

Han, Daolan; Jian, Jinbao; Li, Jie

doi:10.1016/j.na.2011.01.024

Cited by 10 publications

(4 citation statements)

References 15 publications

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“…[ 28 ] described a technique based on the algebraic representation of the constraint set, which identifies active constraints in a neighborhood of a solution. The extension to constrained minimax problems was also first presented in [ 30 ] without strict complementarity and linear independence. Moreover, the identification technique of active constraints for constrained minimax problems can be more suitable for infeasible algorithms, such as the strongly sub-feasible direction method and the penalty function method.…”

Section: Introductionmentioning

confidence: 99%

“…The aim of this paper is to propose such an algorithm, analyze its convergence properties, and report its numerical performance. Motivated by [ 26 , 30 ], in this paper, we propose a generalized gradient projection algorithm directly on with a new working set for the problem ( 1 ). The characteristics of our proposed algorithm can be summarized as follows: We propose a new optimal identification function for the stationary point, from which we provide a new working set.…”

Section: Introductionmentioning

confidence: 99%

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A generalized gradient projection method based on a new working set for minimax optimization problems with inequality constraints

Zhang

Liu

2017

J Inequal Appl

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Combining the techniques of the working set identification and generalized gradient projection, we present a new generalized gradient projection algorithm for minimax optimization problems with inequality constraints. In this paper, we propose a new optimal identification function, from which we provide a new working set. At each iteration, the improved search direction is generated by only one generalized gradient projection explicit formula, which is simple and could reduce the computational cost. Under some mild assumptions, the algorithm possesses the global and strong convergence. Finally, the numerical results show that the proposed algorithm is promising.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A generalized gradient projection method based on a new working set for minimax optimization problems with inequality constraints

Zhang

Liu

2017

J Inequal Appl

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“…Problems with inequality constraints can be reformulated in the above form by introducing slack variables. Moreover, nonlinear constrained programming is significant for solving engineering optimization problems in other forms, for example, the minimax problems (Jian, Quan, and Zhang 2007;Wang and Zhang 2008;Han, Jian, and Li 2011;Jian et al 2014) and dynamic optimization problems (Hu, Ong, and Teo 2002;Mohammed and Zhang 2013;Liu, Li, and Liu 2015;Zhang et al 2015). The filter method, as an alternative to merit functions for nonlinear constrained programming, was first proposed by Fletcher and Leyffer (2002).…”

Section: Introductionmentioning

confidence: 99%

An efficient interior-point algorithm with new non-monotone line search filter method for nonlinear constrained programming

Wang

Liu

Zhang

2016

Engineering Optimization

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An efficient primal-dual interior-point algorithm using a new nonmonotone line search filter method is presented for nonlinear constrained programming, which is widely applied in engineering optimization. The new non-monotone line search technique is introduced to lead to relaxed step acceptance conditions and improved convergence performance. It can also avoid the choice of the upper bound on the memory, which brings obvious disadvantages to traditional techniques. Under mild assumptions, the global convergence of the new non-monotone line search filter method is analysed, and fast local convergence is ensured by second order corrections. The proposed algorithm is applied to the classical alkylation process optimization problem and the results illustrate its effectiveness. Some comprehensive comparisons to existing methods are also presented. ARTICLE HISTORY

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“…a constrained differentiable optimization problem. By transforming (1) into the nonlinear programming problem (2) we can solve it by well-established methods such as feasible-directions algorithms [35], sequential quadratic programming type algorithms [9,13,14,24,45], active set methods [10], interior point methods [22,26,42] and conjugate gradient methods in conjunction with exact penalties and smoothing [48]. Another method is that Problem (1) is reduced to a standard unconstrained smooth optimization problem by using an exponential penalty function…”

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confidence: 99%

Substitution secant/finite difference method to large sparse minimax problems

Li¹,

Gao²,

Dai³

et al. 2014

Journal of Industrial &Amp; Management Optimization

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We present a substitution secant/finite difference (SSFD) method to solve the finite minimax optimization problems with a number of functions whose Hessians are often sparse, i.e., these matrices are populated primarily with zeros. By combining of a substitution method, a secant method and a finite difference method, the gradient evaluations can be employed as efficiently as possible in forming quadratic approximations to the functions, which is more effective than that for large sparse unconstrained differentiable optimization. Without strict complementarity and linear independence, local and global convergence is proven and q-superlinear convergence result and r-convergence rate estimate show that the method has a good convergence property. A handling method of a nonpositive definitive Hessian is given to solve nonconvex problems. Our numerical tests show that the algorithm is robust and quite effective, and that its performance is comparable to or better than that of other algorithms available.

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On the accurate identification of active set for constrained minimax problems

Cited by 10 publications

References 15 publications

A generalized gradient projection method based on a new working set for minimax optimization problems with inequality constraints

A generalized gradient projection method based on a new working set for minimax optimization problems with inequality constraints

An efficient interior-point algorithm with new non-monotone line search filter method for nonlinear constrained programming

Substitution secant/finite difference method to large sparse minimax problems

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