ISSN:
1573-2916
Keywords:
Nonlinear programming
;
global optimization
;
d.c. programming
;
outer approximation
;
system of d.c. inequalities
;
(ɛ, η)-solution
;
fuel mixture problem
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01106607
Permalink
