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Convex relaxations of non-convex mixed integer quadratically constrained programs: extended formulations

2010
*
Mathematical programming
*

This paper addresses the problem

doi:10.1007/s10107-010-0371-9
fatcat:w4c5rkcadrh4po6bsj7lgeiqrm
*of*generating strong*convex**relaxations**of**Mixed**Integer**Quadratically**Constrained**Programming*(MIQCP) problems. ... MIQCP problems are very difficult because they combine two kinds*of**non*-*convexities*:*integer*variables and*non*-*convex**quadratic*constraints. ... student at Tepper School*of*Business, Carnegie Mellon University. ...##
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Convex relaxations of non-convex mixed integer quadratically constrained programs: projected formulations

2010
*
Mathematical programming
*

A common way to produce a

doi:10.1007/s10107-010-0340-3
fatcat:vajnwliitjcb7mrc4p7dya6jq4
*convex**relaxation**of*a*Mixed**Integer**Quadratically**Constrained**Program*(MIQCP) is to lift the problem into a higher dimensional space by introducing variables Y ij to represent ... One advantage*of*such*extended**relaxations*is that they can be efficiently strengthened by using the (*convex*) SDP constraint Y − xx T 0 and disjunctive*programming*. ... We are grateful to Sam Burer for providing us the box-QP instances and their MIQCP-SDP*formulations*. ...##
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Extended formulations in mixed integer conic quadratic programming

2016
*
Mathematical Programming Computation
*

In this paper we consider the use

doi:10.1007/s12532-016-0113-y
fatcat:kznbqi3uing7feu6uac36iu5km
*of**extended**formulations*in LP-based algorithms for*mixed**integer*conic*quadratic**programming*(MICQP). ...*mixed**integer**programming*problems that include general MICQP problems. ... Acknowledgemensts We thank the review team for their thoughtful and constructive comments, which improved the exposition*of*the paper. ...##
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Compact extended formulations for low-rank functions with indicator variables
[article]

2021
*
arXiv
*
pre-print

We study the

arXiv:2110.14884v1
fatcat:w7gkgc44bnbmbg64qomtfkxevq
*mixed*-*integer*epigraph*of*a low-rank*convex*function with*non*-*convex*indicator constraints, which are often used to impose logical constraints on the support*of*the solutions. ...*Extended**formulations*describing the*convex*hull*of*such sets can easily be constructed via disjunctive*programming*, although a direct application*of*this method often yields prohibitively large*formulations*... Such*extended**formulations*are the strongest possible for the*mixed*-*integer*set under study. ...##
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Non-convex mixed-integer nonlinear programming: A survey

2012
*
Surveys in Operations Research and Management Science
*

A wide range

doi:10.1016/j.sorms.2012.08.001
fatcat:ykgvnv2a6jd57lrhjh4qtxd4pi
*of*problems arising in practical applications can be*formulated*as*Mixed*-*Integer*Nonlinear*Programs*(MINLPs). ... We survey the literature on*non*-*convex*MINLP, discussing applications, algorithms and software. Special attention is paid to the case in which the objective and constraint functions are*quadratic*. ... [126, 127] have derived strong cutting planes for*non*-*convex*MIQCQPs (*mixed*-*integer**quadratically**constrained**quadratic**programs*). ...##
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Convex Mixed-Integer Nonlinear Programs Derived from Generalized Disjunctive Programming using Cones
[article]

2021
*
arXiv
*
pre-print

We propose the

arXiv:2109.09657v1
fatcat:yqvnk5nokrajzkbkwl7lkv7ree
*formulation**of**convex*Generalized Disjunctive*Programming*(GDP) problems using conic inequalities leading to conic GDP problems. ... We then show the reformulation*of*conic GDPs into*Mixed*-*Integer*Conic*Programming*(MICP) problems through both the Big-M and Hull Reformulations. ... , Simulation Based Engineering*Program*through the Institute for the Design*of*Advanced Energy Systems (IDAES). ...##
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A Tight SDP Relaxation for MIQCQP Problems in Power Systems Based on Disjunctive Programming
[article]

2015
*
arXiv
*
pre-print

An optimization problem considering AC power flow constraints and

arXiv:1509.05141v1
fatcat:cqeefwerhfd2jbkqo3pifqtcbq
*integer*decision variables can usually be posed as a*mixed*-*integer**quadratically**constrained**quadratic**program*(MIQCQP) problem. ... that an enhanced*mixed*-*integer*SDP (MISDP)*relaxation*, which is a*mixed*-*integer**convex*problem, is obtained. ...*Mixed*-*integer**convex**Mixed*-*integer**convex**Convex**Convex**Convex* MIQCQP GDP *Mixed*-*integer**convex*=*Mixed*-*integer**convex*E. ...##
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Extending the QCR method to general mixed-integer programs

2010
*
Mathematical programming
*

This reformulation, that we call MIQCR (

doi:10.1007/s10107-010-0381-7
fatcat:7uqbfsabfnc2jb63kveu2fy7ga
*Mixed**Integer**Quadratic**Convex*Reformulation), is based on the solution*of*an SDP*relaxation**of*(M QP ). ... Our contribution in this work is to*extend*the ideas*of*QCR (*Quadratic**Convex*Reformulation) [2, 3] from the binary case to the general*mixed*-*integer*case. ... Introduction Consider the following linearly-*constrained**mixed*-*integer**quadratic**program*: (M QP ) 8 > > > > > > > > < > > > > > > > > : M in h(x) s.t. ...##
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The N-K Problem in Power Grids: New Models, Formulations and Numerical Experiments (extended version)
[article]

2009
*
arXiv
*
pre-print

The case where k is small is

arXiv:0912.5233v2
fatcat:c4inm2je6zd4pnky2e5pcngvii
*of*practical interest. We present theoretical and computational results involving a*mixed*-*integer*model and a continuous nonlinear model related to this question. ... a set*of*k or fewer arcs whose removal will cause the system to fail. ... A better*mixed*-*integer**programming**formulation*As before, let A be an attack and C a (given) configuration*of*generators. ...##
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Traces of the XII Aussois Workshop on Combinatorial Optimization

2010
*
Mathematical programming
*

"

doi:10.1007/s10107-010-0369-3
fatcat:b7slvsqv4ncy7j45l3u4dcilz4
*Convex**Relaxations**of**Non*-*Convex**Mixed**Integer**Quadratically**Constrained**Programs*:*Extended**formulations*" by Anureet Saxena, Pierre Bonami, and Jon Lee proposes a method to generate strong*convex**relaxations*...*of**Mixed**Integer**Quadratically**Constrained**programming*problems. ...##
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Introductory mathematical programming for EC

2022
*
Proceedings of the Genetic and Evolutionary Computation Conference Companion
*

• Global optimization has been for several decades addressed by algorithms and Mathematical

doi:10.1145/3520304.3533630
fatcat:oq47iyyzlvf5vevwyquxnwo6py
*Programming*(MP) -branded as Operations Research (OR), yet rooted at Theoretical CS [1] . • Also -it has been ... (LP) 2*integer**programming*(IP) 3*mixed*-*integer**programming*(MIP) 4*quadratic**programming*(QP) and*mixed*-*integer*QP (MIQP) Ofer Shir Introductory MathProg for EC GECCO'22 7 / 56 Ofer Shir Ofer Shir Introductory ...*Program*(QCP) has*quadratic*terms in its constraints (possibly no*quadratic*terms in the objective) •*Mixed*-*integer*QP and QCP involve also*integer*decision variables • Renowned MIQP: the*quadratic*assignment ...##
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Implementation of Mixed-integer Programming on Embedded System

2015
*
Procedia Engineering
*

For systems with binary input variables the

doi:10.1016/j.proeng.2015.01.539
fatcat:qjlfcbcjwfasjfwhohf4nho344
*quadratic*problem is replaced by more challenging*Mixed*-*Integer**Quadratic**Programming*(MIQP) problem. ... One*of*the most widespread modern control strategies is the discrete-time Model Predictive Control (MPC) method which requires the solution*of*the*quadratic**programming*problem. ... MSMT-7778/2014 by the Ministry*of*Education*of*the Czech Republic and also by the European Regional Development Fund under the Project CEBIA-Tech No. CZ.1.05/2.1.00/03.0089. ...##
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Conic mixed-integer rounding cuts

2008
*
Mathematical programming
*

Our computational experiments show that conic

doi:10.1007/s10107-008-0239-4
fatcat:cgfxok6ydfga5mll2amqb5vgoa
*mixed*-*integer*rounding cuts are very effective in reducing the integrality gap*of*continuous*relaxations**of*conic*mixed*-*integer**programs*and, hence, improving ... These cuts can be readily incorporated in branch-and-bound algorithms that solve either second-order conic*programming*or linear*programming**relaxations**of*conic*integer**programs*at the nodes*of*the branch-and-bound ... such as*convex**quadratically**constrained**quadratic**programs*and semidefinite*programs*. ...##
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QPLIB: a library of quadratic programming instances

2018
*
Mathematical Programming Computation
*

.: Semidefinite

doi:10.1007/s12532-018-0147-4
fatcat:7q7dunjewffb3ca2am6kmuf4im
*relaxations*for*non*-*convex**quadratic**mixed*-*integer**programming*. Mathematical*Programming*141(1), 435-452 (2013) 28. Burer, S.: Copositive*programming*. In: F.M. Anjos, B.J. ... This is illustrated by the fact that the class*of*problems that we simply refer to here as "QP" might more accurately be called*Mixed*-*Integer**Quadratically*-*Constrained**Quadratic**Programming*(MIQCQP) in ... Any blank lines, or lines starting with any*of*the characters !, % or # are ignored. Each term in the first column*of*Table 8 denotes a required value. ...##
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An Iterative Method for Nonconvex Quadratically Constrained Quadratic Programs
[article]

2016
*
arXiv
*
pre-print

This paper examines the nonconvex

arXiv:1609.02609v1
fatcat:lv2ayxbhabajtgoovitzggmg6a
*quadratically**constrained**quadratic**programming*(QCQP) problems using an iterative method. ... Each iteration*of*IRM is*formulated*as a*convex*problem with semidefinite constraints. ...*Mixed*-Boolean*Quadratic**Programming*In this subsection, the proposed IRM method is applied to solve*mixed*-boolean*quadratic**programming*problems*formulated*as, J = min x T Q 0 x s.t. x T Q i x + c i ≤ ...
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