Thai Quynh Phong, Pham Dinh Tao, Le Thi Hoai An: "A New Method for Solving D.C. Programming Problem. Application to Fuel Mixture Nonconvex Optimization Problem".

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

     c* = min<c,x> s.t. fi(x) <= 0, i=1,...,m, x∈D} 

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

    x(ε,η)∈D, ⟨c,x(ε,η)⟩ <= c+ε,fi(x(ε,η)) <= η,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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Citation: Thai Quynh Phong, Pham Dinh Tao and Le Thi Hoai An, A New Method for Solving D.C. Programming Problem. Application to Fuel Mixture Nonconvex Optimization Problem. Journal of Global Optimization 6, pp. 87-105,  1995.

 

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