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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 ... We show how the extended*formulation*can be algorithmically*projected*to the original space by solving linear*programs*. ... We are grateful to Sam Burer for providing us the box-QP instances and their MIQCP-SDP*formulations*. ...##
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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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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 ). ... (M QP ) belongs to the class*of**Mixed**Integer**Non*Linear*Programs*(MINLP). These problems are N P-hard [12]. ... Introduction Consider the following linearly-*constrained**mixed*-*integer**quadratic**program*: (M QP ) 8 > > > > > > > > < > > > > > > > > : M in h(x) s.t. ...##
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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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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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A low-cost alternating projection approach for a continuous formulation of convex and cardinality constrained optimization
[article]

2022
*
arXiv
*
pre-print

We consider

arXiv:2209.02756v1
fatcat:y2bu4u7twzb2tmxxoevkixtjii
*convex**constrained*optimization problems that also include a cardinality constraint. ... We assume that the region defined by the*convex*constraints can be written as the intersection*of*a finite collection*of**convex*sets, such that it is easy and inexpensive to*project*onto each one*of*them ... The second author was financially supported by Fundação para a Ciência e a Tecnologia (FCT) (Portuguese Foundation for Science and Technology) under the scope*of*the*projects*UIDB/MAT/00297/2020, UIDP/ ...##
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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. ... Acknowledgements The work was performed with financial support*of*research*project*NPU I No. ...##
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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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Introductory mathematical programming for EC

2022
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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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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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Cuts for mixed 0-1 conic programming

2005
*
Mathematical programming
*

We show that many

doi:10.1007/s10107-005-0578-3
fatcat:myzj3jb2dfegjacyimdhnudtji
*of*the techniques developed for generating linear cuts for*mixed*0-1 linear*programs*, such as the Gomory cuts, the lift-and-*project*cuts, and cuts from other hierarchies*of*tighter*relaxations*... We also show that simple extensions*of*these techniques lead to methods for generating*convex**quadratic*cuts. ... For a more detailed discussion*of**convex**quadratic*cuts for MCPs see [14] . Stubbs and Mehrotra [43] investigate*convex**quadratic*inequalities in the context*of**mixed*0-1*convex**programs*. ...##
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Protein Threading Based on Nonlinear Integer Programming
[article]

2013
*
arXiv
*
pre-print

Actually, the existing linear

arXiv:1310.0395v1
fatcat:tmyp73lprbel7lwpjfgubindeq
*integer**programming*is directly linearized from the original*quadratic**integer**programming*. We then develop corresponding efficient algorithms. ... The most popular algorithm is based on linear*integer**programming*. In this paper, we consider methods based on nonlinear*integer**programming*. ... Linearization strategies are to reformulate the zero-one*quadratic**programs*as equivalent*mixed*-*integer**programming*problems (1.1) and (1.3) with additional binary variables and/or continuous variables ...##
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Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

2016
*
European Journal of Operational Research
*

This manuscript reviews recent advances in deterministic global optimization for

doi:10.1016/j.ejor.2015.12.018
fatcat:jwe7b7ivrzhrjbttdl74eff2pe
*Mixed*-*Integer*Nonlinear*Programming*(MINLP), as well as*Constrained*Derivative-Free Optimization (CDFO). ... We show their individual prerequisites,*formulations*and applicability, but also point out possible points*of*interaction in problems which contain hybrid characteristics. ... MIQCQP, MIQCP, QAP, Box-*Constrained*MIQP A*mixed*-*integer**quadratically*-*constrained**quadratic**program*(MIQCQP) is defined as a MINLP where all*of*the nonlinearities are*quadratic*; symbols have the same ...
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