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A modified verson of Tuy’s method for solving d.c. programming problems. (English) Zbl 0662.90069

The author presents an algorithm to solve the following d.c. programming problem: min cx subject to h(x)\(\leq 0\), g(x)\(\leq 0\) where \(h:R^ n\to R^ 1\) is a continuous convex function and \(g:R^ n\to R^ 1\) is a continuous concave function. The algorithm is a combination of H. Tuy’s method [North-Holland Math. Stud. 129, 273-303 (1986; Zbl 0623.65067)] and J. E. Kelley’s method [SIAM J. Appl. Math. 8, 703- 712 (1960; Zbl 0098.121)]. The author claims that unlike Tuy’s method the present algorithm does not require the solution set to be non-empty. The paper contains some details about the implementation of the algorithm and the working of the algorithm is illustrated by an example. The computational results concerning some test problems are also reported.
Reviewer: R.N.Kaul

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
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References:

[1] DOI: 10.1137/0108053 · Zbl 0098.12104
[2] Nguyen V.H., Technical Report n{\(\deg\)} 85/5. Department of Mathematics (1985)
[3] Shor N.Z., Minimization Methods for Non-Differentiable Functions (1985) · Zbl 0561.90058
[4] Thieu, Presented at the IFIP Working Conference on Recent Advances on System Modelling and Optimization (1983)
[5] Thoai N.V., Seminarherichte n{\(\deg\)} 63 (1984)
[6] Thoai N.V., CORE Discussion Paper 8505 (1985)
[7] Tuy H., On Outer Approximation Methods for Solving Concave Minimization Problems 108 (1983) · Zbl 0574.90074
[8] Tuy H., Presented at the Fermat Days:Mathematics for Optimization (1985)
[9] DOI: 10.1016/0167-6377(88)90071-5 · Zbl 0644.90085
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