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Noname manuscript No. (will be inserted by the editor) On Sublinear Inequalities for Mixed Integer Conic Programs
, 2014
"... Abstract This paper studies Ksublinear inequalities, a class of inequalities with strong relations to Kminimal inequalities for disjunctive conic sets. We establish a stronger result on the sufficiency of Ksublinear inequalities. That is, we show that when K is the nonnegative orthant or the seco ..."
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—so called cutgenerating functions. As a consequence of the sufficiency of Rn+sublinear inequalities, we also provide an alternate and straightforward proof of the sufficiency of cutgenerating functions for mixed integer linear programs, a result recently established by Cornuéjols, Wolsey and Yıldız. 1
On Minimal Valid Inequalities for Mixed Integer Conic Programs
"... We study disjunctive conic sets involving a general regular (closed, convex, full dimensional, and pointed) cone K such as the nonnegative orthant, the Lorentz cone, or the positive semidefinite cone. In a unified framework, we introduce Kminimal inequalities and show that, under mild assumptions, ..."
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Cited by 4 (0 self)
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of the results from the mixed integer linear case. It is well known that the minimal inequalities for mixed integer linear programs are generated by sublinear (positively homogeneous, subadditive, and convex) functions which are also piecewise linear. Our analysis easily recovers this result. However
On Minimal Valid Inequalities for Mixed Integer Conic Programs
, 2013
"... We study mixed integer conic sets involving a general regular (closed, convex, full dimensional, and pointed) cone K such as the nonnegative orthant, the Lorentz cone or the positive semidefinite cone. In a unified framework, we introduce Kminimal inequalities and show that under mild assumptions, ..."
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our framework can be applied. Our framework generalizes the results from the mixed integer linear case, such as the minimal inequalities for mixed integer linear programs are generated by sublinear (positively homogeneous, subadditive and convex) functions that are also piecewise linear. So whenever
Control of Systems Integrating Logic, Dynamics, and Constraints
 Automatica
, 1998
"... This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and ..."
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Cited by 413 (50 self)
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reference trajectories while fulfilling operating constraints, and possibly take into account previous qualitative knowledge in the form of heuristic rules. Due to the presence of integer variables, the resulting online optimization procedures are solved through Mixed Integer Quadratic Programming (MIQP
Lifting for conic mixedinteger programming
, 2011
"... Lifting is a procedure for deriving valid inequalities for mixedinteger sets from valid inequalities for suitable restrictions of those sets. Lifting has been shown to be very effective in developing strong valid inequalities for linear integer programming and it has been successfully used to sol ..."
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Cited by 15 (4 self)
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Lifting is a procedure for deriving valid inequalities for mixedinteger sets from valid inequalities for suitable restrictions of those sets. Lifting has been shown to be very effective in developing strong valid inequalities for linear integer programming and it has been successfully used
Mixing MixedInteger Inequalities
 MATHEMATICAL PROGRAMMING
, 1998
"... Mixedinteger rounding (MIR) inequalities play a central role in the development of strong cutting planes for mixedinteger programs. In this paper, we investigate how known MIR inequalities can be combined in order to generate new strong valid inequalities. Given a mixedinteger region S and a coll ..."
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Cited by 25 (2 self)
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Mixedinteger rounding (MIR) inequalities play a central role in the development of strong cutting planes for mixedinteger programs. In this paper, we investigate how known MIR inequalities can be combined in order to generate new strong valid inequalities. Given a mixedinteger region S and a
Conic mixedinteger rounding cuts
 University of CaliforniaBerkeley
, 2006
"... Abstract. A conic integer program is an integer programming problem with conic constraints. Many important problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints. Here we study mixedinteger sets defined by secondorder conic constr ..."
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Cited by 21 (4 self)
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Abstract. A conic integer program is an integer programming problem with conic constraints. Many important problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints. Here we study mixedinteger sets defined by secondorder conic
Strong Dual for Conic MixedInteger Programs
, 2011
"... Mixedinteger conic programming is a generalization of mixedinteger linear programming. In this paper, we present an extension of the duality theory for mixedinteger linear programming (see [4], [11]) to the case of mixedinteger conic programming. In particular, we construct a subadditive dual fo ..."
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Cited by 3 (0 self)
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Mixedinteger conic programming is a generalization of mixedinteger linear programming. In this paper, we present an extension of the duality theory for mixedinteger linear programming (see [4], [11]) to the case of mixedinteger conic programming. In particular, we construct a subadditive dual
A lifted linear programming branchandbound algorithm for mixed integer conic quadratic programs
, 2007
"... This paper develops a linear programming based branchandbound algorithm for mixed integer conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by BenTal and Nemirovski. The algorithm is different from o ..."
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Cited by 26 (1 self)
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This paper develops a linear programming based branchandbound algorithm for mixed integer conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by BenTal and Nemirovski. The algorithm is different from
Valid inequalities for mixed integer linear programs
 MATHEMATICAL PROGRAMMING B
, 2006
"... This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as liftandproject cuts, Gomory mixed integer cuts, mixed integ ..."
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Cited by 50 (0 self)
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This tutorial presents a theory of valid inequalities for mixed integer linear sets. It introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as liftandproject cuts, Gomory mixed integer cuts, mixed
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