Duality for Mixed Integer Linear Programs
نویسندگان
چکیده
The theory of duality for linear programs is well-developed and has been successful in advancing both the theory and practice of linear programming. In principle, much of this broad framework can be extended to mixed integer linear programs, but this has proven difficult, in part because duality theory does not integrate well with current computational practice. This paper surveys what is known about duality for integer programs and offers some minor extensions, with an eye towards developing a more practical framework.
منابع مشابه
Strong Dual for Conic Mixed-Integer Programs∗
Mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension of the duality theory for mixed-integer linear programming (see [4], [11]) to the case of mixed-integer conic programming. In particular, we construct a subadditive dual for mixed-integer conic programming problems. Under a simple condition on the primal problem, we ar...
متن کاملSecond-Order Symmetric Duality for Minimax Mixed Integer Programs over Cones
A duality theorem for a pair of Wolfe-type second-order minimax mixed integer symmetric dual programs over cones is proved under separability and η-bonvexity/η-boncavity of the function k(x, y) appearing in the objective, where : . n m k R R R × ֏ Mond-Weir type symmetric duality over cones is also studied under η-pseudobonvexity/ηpseudoboncavity assumptions. Self duality (when the dual proble...
متن کاملCertificates of Optimality and Sensitivity Analysis Using Generalized Subadditive Generator Functions: a Test Study on Knapsack Problems
We introduce a family of subadditive functions called Generator Functions for mixed integer linear programs. These functions were previously defined for pure integer programs with non-negative entries by Klabjan [13]. They are feasible in the subadditive dual and we show that they are enough to achieve strong duality. Several properties of the functions are shown. We then use this class of func...
متن کاملSecond order symmetric duality for nonlinear multiobjective mixed integer programming
9 Abstract 10 We formulate two pairs of second order symmetric duality for nonlinear multiobjective mixed integer programs for 11 arbitrary cones. By using the concept of efficiency and second order invexity, we establish the weak, strong, converse 12 and self-duality theorems for our dual models. Several known results are obtained as special cases. 17 Following the earlier works of Dorn [5], D...
متن کاملGlobal optimization of mixed-integer nonlinear programs: A theoretical and computational study
This work addresses the development of an efficient solution strategy for obtaining global optima of continuous, integer, and mixed-integer nonlinear programs. Towards this end, we develop novel relaxation schemes, range reduction tests, and branching strategies which we incorporate into the prototypical branch-and-bound algorithm. In the theoretical/algorithmic part of the paper, we begin by d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006