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A method for solving d.c. programming problems. Application to fuel mixture nonconvex optimization problem

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Abstract

We present a numerical method for solving the d.c. programming problem

$$c^* = \min \{ \langle c,x\rangle s.t. f_i (x) \leqslant 0, i = 1,...,m, x \in D\} $$

wherefi, i=1,...,m are d.c. (difference of two convex functions) and D is a convex set in ℝn. An (ɛ, η)-solutionx(ɛ, η) satisfying

$$x(\varepsilon ,\eta ) \in D, \langle c,x(\varepsilon ,\eta )\rangle \leqslant c^* + \varepsilon , f_i (x(\varepsilon ,\eta )) \leqslant \eta , i = 1,...,m,$$

can be found after a finite number of iterations. This algorithm combines an outer approximation procedure for solving a system of d.c. inequalities with a simple general scheme for minimizing a linear function over a compact set. As an application we discuss the numerical solution of a fuel mixture problem (encountered in the oil industry).

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Authors and Affiliations

  1. LMI-INSA Rouen, CNRS, URA 1378, B.P. 08, 76131, Mt St Aignan Cedex, France

    Thai Quynh Phong, Pham Dinh Tao & Thi Hoai Le An

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  1. Thai Quynh Phong
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  2. Pham Dinh Tao
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  3. Thi Hoai Le An
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Phong, T.Q., Tao, P.D. & Le An, T.H. A method for solving d.c. programming problems. Application to fuel mixture nonconvex optimization problem. J Glob Optim 6, 87–105 (1995). https://doi.org/10.1007/BF01106607

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  • DOI: https://doi.org/10.1007/BF01106607

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