Lifting Group Inequalities and an Application to Mixing Inequalities∗
نویسندگان
چکیده
Given a valid inequality for the mixed integer infinite group relaxation, a lifting based approach is presented that can be used to strengthen this inequality. Bounds on the solution of the corresponding lifting problem and some necessary conditions for the lifted inequality to be minimal for the mixed integer infinite group relaxation are presented. Finally, these results are applied to generate a strengthened version of the mixing inequality that provides a new class of extreme inequalities for the two-row mixed integer infinite group relaxation.
منابع مشابه
Composite lifting of group inequalities and an application to two-row mixing inequalities
Given a valid inequality for the mixed integer infinite group relaxation, a composite lifting approach that combines sequential lifting and use of a fill-in function is proposed that can be used to strengthen this inequality. Properties of this composite lifting such as bounds on the solution of the lifting problem and some necessary conditions for the lifted inequality to be minimal for the mi...
متن کاملStrong Inequalities for Chance–Constrained Programming
As an essential substructure underlying a large class of chance-constrained programming problems with finite discrete distributions, the mixing set with 0 − 1 knapsack has received considerable attentions in recent literature. In this study, we present a family of strong inequalities that subsume known inequalities for this set. We also find many other inequalities that can be explained by lift...
متن کاملA polyhedral study on chance constrained program with random right-hand side
The essential structure of the mixed–integer programming formulation for chance–constrained program (CCP) with stochastic right–hand side is the intersection of multiple mixing sets with a 0− 1 knapsack. To improve our computational capacity on CCP, an underlying substructure, the (single) mixing set with a 0 − 1 knapsack, has received substantial attentions recently. In this study, we first pr...
متن کاملNew Inequalities for Finite and Infinite Group Problems from Approximate Lifting
In this paper, we derive new families of piecewise linear facet-defining inequalities for the finite group problem and extreme inequalities for the infinite group problem using approximate lifting. The new valid inequalities for the finite group problem are twoand three-slope facet-defining inequalities as well as the first family of four-slope facet-defining inequalities. The new valid inequal...
متن کاملMoment Inequalities for Supremum of Empirical Processes of U-Statistic Structure and Application to Density Estimation
We derive moment inequalities for the supremum of empirical processes of U-Statistic structure and give application to kernel type density estimation and estimation of the distribution function for functions of observations.
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 2009