Journal of Global Optimization

, Volume 6, Issue 1, pp 87–105 | Cite as

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

  • Thai Quynh Phong
  • Pham Dinh Tao
  • Thi Hoai Le An


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).

Key words

Nonlinear programming global optimization d.c. programming outer approximation system of d.c. inequalities (ɛ, η)-solution fuel mixture problem 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Thai Quynh Phong
    • 1
  • Pham Dinh Tao
    • 1
  • Thi Hoai Le An
    • 1
  1. 1.LMI-INSA RouenCNRS, URA 1378Mt St Aignan CedexFrance

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