ISSN:
1573-2878
Keywords:
Global optimization
;
nonconvex programming
;
mathematical programming
;
concave minimization
;
DC-programming
;
Lipschitzian optimization
;
branch-and-bound methods
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A crucial problem for many global optimization methods is how to handle partition sets whose feasibility is not known. This problem is solved for broad classes of feasible sets including convex sets, sets defined by finitely many convex and reverse convex constraints, and sets defined by Lipschitzian inequalities. Moreover, a fairly general theory of bounding is presented and applied to concave objective functions, to functions representable as differences of two convex functions, and to Lipschitzian functions. The resulting algorithms allow one to solve any global optimization problem whose objective function is of one of these forms and whose feasible set belongs to one of the above classes. In this way, several new fields of optimization are opened to the application of global methods.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00939768
