Disjunctive Cuts for Mixed Integer Nonlinear Programming Problems
نویسندگان
چکیده
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.
منابع مشابه
Mixed integer programming with a class of nonlinear convex constraints
We study solution approaches to a class of mixed-integer nonlinear programming problems that arise from recent developments in risk-averse stochastic optimization and contain second-order and p-order cone programming as special cases. We explore possible applications of some of the solution techniques that have been successfully used in mixed-integer conic programming and show how they can be g...
متن کاملCutting Planes for Mixed Integer Programming
The purpose of this paper is to present an overview of families of cutting planes for mixed integer programming problems. We examine the families of disjunctive inequalities, split cuts, mixed integer rounding inequalities, mixed integer Gomory cuts, intersection cuts, lift-and-project cuts, and reduceand-split cuts. In practice, mixed integer Gomory cuts are very useful in obtaining solutions ...
متن کاملDisjunctive Cuts for Nonconvex Minlp
Mixed Integer Nonlinear Programming (MINLP) problems present two main challenges: the integrality of a subset of variables and nonconvex (nonlinear) objective function and constraints. Many exact solvers for MINLP are branch-and-bound algorithms that compute a lower bound on the optimal solution using a linear programming relaxation of the original problem. In order to solve these problems to o...
متن کاملSufficient global optimality conditions for general mixed integer nonlinear programming problems
In this paper, some KKT type sufficient global optimality conditions for general mixed integer nonlinear programming problems with equality and inequality constraints (MINPP) are established. We achieve this by employing a Lagrange function for MINPP. In addition, verifiable sufficient global optimality conditions for general mixed integer quadratic programming problems are der...
متن کاملComputations with disjunctive cuts for two-stage stochastic mixed 0-1 integer programs
Two-stage stochastic mixed-integer programming (SMIP) problems with recourse are generally difficult to solve. This paper presents a first computational study of a disjunctive cutting plane method for stochastic mixed 0-1 programs that uses lift-and-project cuts based on the extensive form of the two-stage SMIP problem. An extension of the method based on where the data uncertainty appears in t...
متن کامل