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Mixed Integer Programming Computation
The first 50 years of Integer and Mixed-Integer Programming have taken us to a very stable paradigm for solving problems in a reliable and effective way. We run over these 50 exciting years by showing some crucial milestones and we highlight the building
Lodi A., Andrea Lodi, Lodi, Andrea
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Extended Formulations in Mixed-Integer Convex Programming [PDF]
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP).
Vielma, Juan Pablo +3 more
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Mixed Integer Linear Programming for Mixed Integer Quadratic Programming
National audienceAbstract. In this paper we consider the mixed integer general quadratic problem (MIGQP) that consists in maximizing a quadratic function subject to quadratic constraints, with three types of variables: binary, integer and real.
Billionnet, Alain
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On convergence in mixed integer programming [PDF]
ISSN:1436 ...
Alberto Del Pia, Robert Weismantel
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With a growing percentage of elderly or disabled people in our society, the number of people not being able to drive a car themselves, or even to go by bus, increases, too. Specific services are required to address mobility demands, and dial-a-ride systems have been developed to provide an appropriate answer.
Jon Lee 0001, Adam N. Letchford
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Mixed-integer quadratic programming is in NP [PDF]
Mixed-integer quadratic programming is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete.
Alberto Del Pia +2 more
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Network Formulations of Mixed-Integer Programs [PDF]
We consider mixed-integer sets described by system of linear inequalities in which the constraint matrix A is totally unimodular; the right-hand side is arbitrary vector; and a subset of the variables is required to be integer. We show that the problem of checking nonemptiness of a set of this type is NP-complete, even in the case in which the linear ...
CONFORTI, MICHELANGELO +3 more
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On mixed-integer random convex programs [PDF]
We consider a class of mixed-integer optimization problems subject to N randomly drawn convex constraints. We provide explicit bounds on the tails of the probability that the optimal solution found under these N constraints will become infeasible for the next random constraint.
Giuseppe Carlo Calafiore +2 more
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Mixed-integer programming in motion planning
This paper presents a review of past and present results and approaches in the area of motion planning using MIP (Mixed-integer Programming). Although in the early 2000s MIP was still seen with reluctance as method for solving motion planning-related problems, nowadays, due to increases in computational power and theoretical advances, its extensive ...
Ioan, Daniel +4 more
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Lifting for conic mixed-integer programming [PDF]
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
ATAMTURK, A, NARAYANAN, V
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