Numerical methods for solving a class of global nonconvex optimization problems. (English) Zbl 0683.90077

New methods in optimization and their industrial uses, Proc. Symp., Pau/Fr. and Paris/Fr. 1987, ISNM, Int. Ser. Numer. Math. 87, 97-132 (1989).
Summary: [For the entire collection see Zbl 0679.00019.]
We present a numerical algorithm for solving global optimization problems of the form: \[ (P)\quad Min\{cx:\quad x\in C,\quad g(x)\geq 0\} \] where g and C are convex. It is based on well-known characterizations of optimal solutions for (P) in the case where C is a polytope, and on the well-known principles of outer approximation and of cutting plane. Applying this method to the following classes of global (nonconvex) optimization problems: (1) Min\(\{\) f(x): \(x\in C\}\) where -f and C are convex, (2) Min\(\{\) f(x)-g(x): \(x\in C\}\) where f, g and C are convex, (3) Min\(\{\) f(x): \(x\in C\), g(x)\(\geq 0\}\) where f, g and C are convex, we obtain new interesting algorithms for solving these problems.
Numerical solutions to a fuel mixture nonconvex optimization problem are presented.


90C30 Nonlinear programming
65K05 Numerical mathematical programming methods


Zbl 0679.00019