Discretization in semi-infinite programming: the rate of convergence

Still, Georg J.

doi:10.1007/s101070100239

Cited by 98 publications

(70 citation statements)

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“…We mainly discuss the convergence of asymptotic approximation of the parametric set Y j (j ∈ q) in the sense of Kuratowski This approximate model is different from those of [2,7,8,9], and is their extension to some extent. Thus,we can get the approximation problem of SIMP:…”

Section: Asymptotic Approximation and Its Convergencementioning

confidence: 99%

Asymptotic Approximation Method and Its Convergence on Semi-Infinite Programming

Wan

Wang

et al. 2006

Acta Mathematica Scientia

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The aim of this paper is to discuss an asymptotic approximation model and its convergence for the minimax semi-infinite programming problem. An asymptotic surrogate constraints method for the minimax semi-infinite programming problem is presented making use of two general discrete approximation methods. Simultaneously, we discuss the consistence and the epi-convergence of the asymptotic approximation problem.

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Section: Asymptotic Approximation and Its Convergencementioning

confidence: 99%

Asymptotic Approximation Method and Its Convergence on Semi-Infinite Programming

Wan

Wang

et al. 2006

Acta Mathematica Scientia

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“…In particular, if S = {x} is a singleton, then condition (6.5) coincides with condition (4.22) and hence the above definition is consistent with Definition 4.2. For singleton S the following result is given in [32] (see also [21,Theorem 12]). …”

Section: Rates Of Convergence Of Solutions Of Discretized Problemsmentioning

confidence: 99%

Semi-infinite programming, duality, discretization and optimality conditions†

2009

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“…Many methods have been proposed for the SIP problem. We refer readers to [4,6,11,12,15,17] for details.…”

Section: Introductionmentioning

confidence: 99%

A Truncated Projected Newton-Type Algorithm for Large-Scale Semi-infinite Programming

Qin¹,

Ling²,

Qi³

et al. 2006

SIAM J. Optim.

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Abstract. In this paper, a truncated projected Newton-type algorithm is presented for solving large-scale semi-infinite programming problems. This is a hybrid method of a truncated projected Newton direction and a modified projected gradient direction. The truncated projected Newton method is used to solve the constrained nonlinear system. In order to guarantee global convergence, a robust loss function is chosen as the merit function, and the projected gradient method inserted is used to decrease the merit function. This algorithm is suitable for handling large-scale problems and possesses superlinear convergence rate. The global convergence of this algorithm is proved and the convergence rate is analyzed. The detailed implementation is discussed, and some numerical tests for solving large-scale semi-infinite programming problems, with examples up to 2000 decision variables, are reported.

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Discretization in semi-infinite programming: the rate of convergence

Cited by 98 publications

References 0 publications

Asymptotic Approximation Method and Its Convergence on Semi-Infinite Programming

Asymptotic Approximation Method and Its Convergence on Semi-Infinite Programming

Semi-infinite programming, duality, discretization and optimality conditions†

A Truncated Projected Newton-Type Algorithm for Large-Scale Semi-infinite Programming

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