Error bounds for mixed integer linear optimization problems
نویسنده
چکیده
We introduce computable a-priori and a-posteriori error bounds for optimality and feasibility of a point generated as the rounding of an optimal point of the LP relaxation of a mixed integer linear optimization problem. Treating the mesh size of integer vectors as a parameter allows us to study the effect of different ‘granularities’ in the discrete variables on the error bounds. Our analysis mainly bases on the construction of a so-called grid relaxation retract. Relations to proximity results and the integer rounding property are highlighted.
منابع مشابه
A feasible rounding approach for mixed-integer nonlinear optimization problems
We introduce a new technique to generate good feasible points of mixedinteger nonlinear optimization problems. It makes use of the so-called inner parallel set of the relaxed feasible set, which was employed in O. Stein, Error bounds for mixed integer linear optimization problems, Mathematical Programming, Vol. 156 (2016), 101–123, as well as O. Stein, Error bounds for mixed integer nonlinear o...
متن کاملError bounds for mixed integer nonlinear optimization problems
We introduce a-posteriori and a-priori error bounds for optimality and feasibility of a point generated as the rounding of an optimal point of the NLP relaxation of a mixed-integer nonlinear optimization problem. Our analysis mainly bases on the construction of a tractable approximation of the so-called grid relaxation retract. Under appropriate Lipschitz assumptions on the defining functions, ...
متن کاملA feasible rounding approach for granular optimization problems
We introduce a new technique to generate good feasible points of mixedinteger nonlinear optimization problems which are granular in the sense that a certain inner parallel set of their continuously relaxed feasible set is consistent. The latter inner parallel set was employed in O. Stein, Error bounds for mixed integer linear optimization problems, Mathematical Programming, Vol. 156 (2016), 101...
متن کاملLifting Linear Extension Complexity Bounds to the Mixed-Integer Setting
Mixed-integer mathematical programs are among the most commonly used models for a wide set of problems in Operations Research and related fields. However, there is still very little known about what can be expressed by small mixed-integer programs. In particular, prior to this work, it was open whether some classical problems, like the minimum odd-cut problem, can be expressed by a compact mixe...
متن کاملGlobal Solution Strategies for the Network-Constrained Unit Commitment (NCUC) Problem with Nonlinear AC Transmission Models
This paper addresses the globally optimal solution of the network-constrained unit commitment (NCUC) problem incorporating a nonlinear alternating current (AC) model of the transmission network. We formulate the NCUC as a mixed-integer quadratically constrained quadratic programming (MIQCQP) problem. A global optimization algorithm is developed based on a multi-tree approach that iterates betwe...
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:
- Math. Program.
دوره 156 شماره
صفحات -
تاریخ انتشار 2016