Intersection cuts for nonlinear integer programming: convexification techniques for structured sets
نویسندگان
چکیده
منابع مشابه
Intersection cuts for nonlinear integer programming: convexification techniques for structured sets
We study the generalization of split and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference of two convex sets with specific geometric structures. We introduce two techniques to give precise characterizations of such convex hulls and use them to construct split...
متن کاملIntersection Cuts for Mixed Integer Conic Quadratic Sets
Balas introduced intersection cuts for mixed integer linear sets. Intersection cuts are given by closed form formulas and form an important class of cuts for solving mixed integer linear programs. In this paper we introduce an extension of intersection cuts to mixed integer conic quadratic sets. We identify the formula for the conic quadratic intersection cut by formulating a system of polynomi...
متن کاملDisjunctive Cuts for Mixed Integer Nonlinear Programming Problems
We survey recent progress in applying disjunctive programming theory for the effective solution of mixed integer nonlinear programming problems. Generation of effective cutting planes is discussed for both the convex and nonconvex cases.
متن کاملSemidefinite Cuts and Partial Convexification Techniques with Applications to Continuous Nonconvex Optimization, Stochastic Integer Programming, and Facility Layout Problems
(ABSTRACT) Despite recent advances in convex optimization techniques, the areas of discrete and continuous nonconvex optimization remain formidable, particularly when globally optimal solutions are desired. Most solution techniques, such as branch-and-bound, are enumerative in nature, and the rate of their convergence is strongly dependent on the accuracy of the bounds provided, and therefore, ...
متن کاملSpherical cuts for integer programming problems
Abstract We introduce a new family of valid inequalities for general linear integer programming problems, based on the distance of the relaxed solution to the closest integral point. We show that these are valid cuts, establish some relations with Balas’ intersection cuts, and show that a straightforward cutting plane algorithm derived from either spherical or intersection cuts will in general ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2015
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-015-0866-5