Mixed Integer Second Order Cone Optimization, Disjunctive Conic Cuts: Theory and experiments

1

[1]  Abel M. Rodrigues.  Matrix Algebra Useful for Statistics , 2007 .

[2]  M. Saltzman,et al.  ALPS : A Framework for Implementing Parallel Search Algorithms , 2004 .

[3]  Ted K. Ralphs,et al.  Integer and Combinatorial Optimization , 2013 .

[4]  Sanjay Mehrotra,et al.  A branch-and-cut method for 0-1 mixed convex programming , 1999, Math. Program..

[5]  Martin W. P. Savelsbergh,et al.  A Computational Study of Search Strategies for Mixed Integer Programming , 1999, INFORMS J. Comput..

[6]  Donal O'Shea,et al.  Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.) , 1997, Undergraduate texts in mathematics.

[7]  Alper Atamtürk,et al.  Lifting for conic mixed-integer programming , 2011, Math. Program..

[8]  Joe W. Harris,et al.  Algebraic Geometry: A First Course , 1995 .

[9]  Ralph E. Gomory,et al.  Outline of an Algorithm for Integer Solutions to Linear Programs and An Algorithm for the Mixed Integer Problem , 2010, 50 Years of Integer Programming.

[10]  Gérard Cornuéjols,et al.  Valid inequalities for mixed integer linear programs , 2007, Math. Program..

[11]  Andrew Zisserman,et al.  Solving Markov Random Fields using Second Order Cone Programming Relaxations , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[12]  Erling D. Andersen,et al.  On implementing a primal-dual interior-point method for conic quadratic optimization , 2003, Math. Program..

[13]  Lisa Turner,et al.  Applications of Second Order Cone Programming , 2012 .

[14]  Arkadi Nemirovski,et al.  Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[15]  Alper Atamtürk,et al.  A Conic Integer Programming Approach to Stochastic Joint Location-Inventory Problems , 2012, Oper. Res..

[16]  Alper Atamtürk,et al.  Conic mixed-integer rounding cuts , 2009, Math. Program..

[17]  D. J. White,et al.  A Lagrangean Relaxation Approach for a Turbine Design Quadratic Assignment Problem , 1996 .

[18]  Kim-Chuan Toh,et al.  SDPT3 -- A Matlab Software Package for Semidefinite Programming , 1996 .

[19]  Egon Balas,et al.  A lift-and-project cutting plane algorithm for mixed 0–1 programs , 1993, Math. Program..

[20]  Gene H. Golub,et al.  Some modified matrix eigenvalue problems , 1973, Milestones in Matrix Computation.

[21]  Mehmet Tolga Çezik,et al.  Cuts for mixed 0-1 conic programming , 2005, Math. Program..

[22]  Ralph E. Gomory,et al.  An algorithm for integer solutions to linear programs , 1958 .

[23]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[24]  Omprakash K. Gupta,et al.  Branch and Bound Experiments in Convex Nonlinear Integer Programming , 1985 .

[25]  François Margot,et al.  Testing cut generators for mixed-integer linear programming , 2009, Math. Program. Comput..

[26]  Arkadi Nemirovski,et al.  On Polyhedral Approximations of the Second-Order Cone , 2001, Math. Oper. Res..

[27]  Fred W. Glover,et al.  The feasibility pump , 2005, Math. Program..

[28]  Matthew J. Saltzman,et al.  Computational Experience with a Software Framework for Parallel Integer Programming , 2009, INFORMS J. Comput..

[29]  Ted K. Ralphs,et al.  Parallel Branch and Cut , 2006 .

[30]  Jean-Paul Chilès,et al.  Wiley Series in Probability and Statistics , 2012 .

[31]  Germán Riaño,et al.  jMarkov: an object-oriented framework for modeling and analyzing Markov chains and QBDs , 2006, SMCtools '06.

[32]  Nelson Maculan,et al.  Using a Conic Formulation for Finding Steiner Minimal Trees , 2004, Numerical Algorithms.

[33]  Leo Liberti,et al.  Branching and bounds tighteningtechniques for non-convex MINLP , 2009, Optim. Methods Softw..

[34]  Gérard Cornuéjols,et al.  An algorithmic framework for convex mixed integer nonlinear programs , 2008, Discret. Optim..

[35]  Pavlo A. Krokhmal,et al.  Risk optimization with p-order conic constraints: A linear programming approach , 2010, Eur. J. Oper. Res..

[36]  A. Mahajan.  ON SELECTING DISJUNCTIONS FOR SOLVING MIXED INTEGER PROGRAMMING PROBLEMS , 2009 .

[37]  J. Mitchell.  Branch-and-Cut Algorithms for Combinatorial Optimization Problems , 1988 .

[38]  Daniel Dadush,et al.  The split closure of a strictly convex body , 2011, Oper. Res. Lett..

[39]  Dimitris Bertsimas,et al.  Algorithm for cardinality-constrained quadratic optimization , 2009, Comput. Optim. Appl..

[40]  S. Leyffer,et al.  More Branch-and-Bound Experiments in Convex Nonlinear Integer Programming , 2011 .

[41]  William J. Cook,et al.  Numerically Safe Gomory Mixed-Integer Cuts , 2009, INFORMS J. Comput..

[42]  P. Lancaster,et al.  The theory of matrices : with applications , 1985 .

[43]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.

[44]  Thorsten Koch,et al.  Branching rules revisited , 2005, Oper. Res. Lett..

[45]  Hans D. Mittelmann,et al.  Interior Point Methods for Second-Order Cone Programming and OR Applications , 2004, Comput. Optim. Appl..

[46]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[47]  Martin W. P. Savelsbergh,et al.  Preprocessing and Probing Techniques for Mixed Integer Programming Problems , 1994, INFORMS J. Comput..

[48]  Julio C. Góez,et al.  A Conic Representation of the Convex Hull of Disjunctive Sets and Conic Cuts for Integer Second Order Cone Optimization , 2015 .

[49]  E. L. Lawler,et al.  Branch-and-Bound Methods: A Survey , 1966, Oper. Res..

[50]  Sinan Gürel,et al.  A strong conic quadratic reformulation for machine-job assignment with controllable processing times , 2009, Oper. Res. Lett..

[51]  Sujeevraja Sanjeevi.  Mixed n-Step MIR Inequalities, n-Step Conic MIR Inequalities and a Polyhedral Study of Single Row Facility Layout Problem , 2012 .

[52]  Donald Goldfarb,et al.  Second-order cone programming , 2003, Math. Program..

[53]  George L. Nemhauser,et al.  A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs , 2008, INFORMS J. Comput..

[54]  Carl D. Meyer,et al.  Matrix Analysis and Applied Linear Algebra , 2000 .

[55]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[56]  S. Ulbrich,et al.  MIXED INTEGER SECOND ORDER CONE PROGRAMMING , 2008 .

[57]  I. Grossmann.  Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques , 2002 .

[58]  Laurence A. Wolsey,et al.  A recursive procedure to generate all cuts for 0–1 mixed integer programs , 1990, Math. Program..

[59]  Jos F. Sturm,et al.  Implementation of interior point methods for mixed semidefinite and second order cone optimization problems , 2002, Optim. Methods Softw..

[60]  Yong Cheng,et al.  Joint network optimization and beamforming for Coordinated Multi-Point Transmission using mixed integer programming , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[61]  Hanif D. Sherali,et al.  Disjunctive Programming , 2009, Encyclopedia of Optimization.

[62]  Alexander Barvinok,et al.  A course in convexity , 2002, Graduate studies in mathematics.

[63]  Alexander Martin,et al.  General Mixed Integer Programming: Computational Issues for Branch-and-Cut Algorithms , 2000, Computational Combinatorial Optimization.

[64]  Pietro Belotti,et al.  On families of quadratic surfaces having fixed intersections with two hyperplanes , 2013, Discret. Appl. Math..

[65]  C. H. Sisam,et al.  Analytic Geometry Of Space , .

[66]  Juan Pablo Vielma Centeno,et al.  Mixed integer programming approaches for nonlinear and stochastic programming , 2009 .