CBLIB 2014: a benchmark library for conic mixed-integer and continuous optimization

The Conic Benchmark Library is an ongoing community-driven project aiming to challenge commercial and open source solvers on mainstream cone support. In this paper, 121 mixed-integer and continuous second-order cone problem instances have been selected from 11 categories as representative for the instances available online. Since current file formats were found incapable, we embrace the new Conic Benchmark Format as standard for conic optimization. Tools are provided to aid integration of this format with other software packages.

[1]  Franz Rendl,et al.  Computational Experience with Ill-Posed Problems in Semidefinite Programming , 2002, Comput. Optim. Appl..

[2]  Timo Berthold,et al.  Extending a CIP framework to solve MIQCPs , 2012 .

[3]  Thorsten Koch.  The final NETLIB-LP results , 2004, Oper. Res. Lett..

[4]  Henry Wolkowicz,et al.  Strong duality and minimal representations for cone optimization , 2012, Computational Optimization and Applications.

[5]  Yinyu Ye,et al.  Warmstarting the homogeneous and self-dual interior point method for linear and conic quadratic problems , 2013, Math. Program. Comput..

[6]  Andrea Lodi,et al.  MIPLIB 2010 , 2011, Math. Program. Comput..

[7]  Etienne de Klerk,et al.  A new library of structured semidefinite programming instances , 2009, Optim. Methods Softw..

[8]  Tamás Terlaky,et al.  New stopping criteria for detecting infeasibility in conic optimization , 2009, Optim. Lett..

[9]  P. Toint,et al.  Testing a class of methods for solving minimization problems with simple bounds on the variables , 1988 .

[10]  James Renegar,et al.  Incorporating Condition Measures into the Complexity Theory of Linear Programming , 1995, SIAM J. Optim..

[11]  Michael L. Overton,et al.  Computing Limit Loads by Minimizing a Sum of Norms , 1998, SIAM J. Sci. Comput..

[12]  Robert J. Vanderbei,et al.  Random-process formulation of computationally efficient performance measures for wideband arrays in the far field , 1999, 42nd Midwest Symposium on Circuits and Systems (Cat. No.99CH36356).

[13]  Pablo A. Parrilo,et al.  Partial facial reduction: simplified, equivalent SDPs via approximations of the PSD cone , 2014, Math. Program..

[14]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .

[15]  Brian Borchers,et al.  SDPLIB 1.1, A Library of Semidefinite Programming Test Problems , 1998 .

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

[17]  John W. Chinneck,et al.  Feasibility And Infeasibility In Optimization , 2015 .

[18]  Philip J. Fleming,et al.  How not to lie with statistics: the correct way to summarize benchmark results , 1986, CACM.

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

[20]  Roland W. Freund,et al.  A sensitivity result for semidefinite programs , 2004, Oper. Res. Lett..

[21]  Juan Pablo Vielma,et al.  A Strong Dual for Conic Mixed-Integer Programs , 2012, SIAM J. Optim..

[22]  S. Kartik Krishnan,et al.  A CONIC INTERIOR POINT DECOMPOSITION APPROACH FOR LARGE SCALE SEMIDEFINITE PROGRAMMING , 2005 .

[23]  Julio C. Góez,et al.  Mixed Integer Second Order Cone Optimization, Disjunctive Conic Cuts: Theory and experiments , 2013 .

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

[25]  Hans Ziegler,et al.  Solving certain singly constrained convex optimization problems in production planning , 1982, Oper. Res. Lett..

[26]  Samir Elhedhli,et al.  Service System Design with Immobile Servers, Stochastic Demand, and Congestion , 2006, Manuf. Serv. Oper. Manag..

[27]  M. Kojima,et al.  SPARSE SECOND ORDER CONE PROGRAMMING FORMULATIONS FOR CONVEX OPTIMIZATION PROBLEMS , 2008 .

[28]  Oktay Günlük,et al.  IBM Research Report MINLP Strengthening for Separable Convex Quadratic Transportation-Cost UFL , 2007 .

[29]  G. Pataki.  Strong Duality in Conic Linear Programming: Facial Reduction and Extended Duals , 2013, 1301.7717.

[30]  Pólik Imre,et al.  Conic Optimization Software , 2011 .

[31]  Miguel F. Anjos,et al.  On Handling Free Variables in Interior-Point Methods for Conic Linear Optimization , 2007, SIAM J. Optim..

[32]  Stephen P. Boyd,et al.  Applications of second-order cone programming , 1998 .

[33]  D.P. Scholnik,et al.  A specification language for the optimal design of exotic FIR filters with second-order cone programs , 2002, Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers, 2002..

[34]  Yurii Nesterov,et al.  Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.

[35]  Jeff T. Linderoth,et al.  Algorithms and Software for Convex Mixed Integer Nonlinear Programs , 2012 .

[36]  Hirokazu Anai,et al.  An effective implementation of a symbolic-numeric cylindrical algebraic decomposition for quantifier elimination , 2009, SNC '09.

[37]  Kim-Chuan Toh,et al.  Solving semidefinite-quadratic-linear programs using SDPT3 , 2003, Math. Program..

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

[39]  Michael J. Todd,et al.  Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems , 1999, Math. Program..

[40]  François Glineur,et al.  Conic optimization: an elegant framework for convex optimization , 2001 .

[41]  Frank Permenter,et al.  Solving Conic Optimization Problems via Self-Dual Embedding and Facial Reduction: A Unified Approach , 2017, SIAM J. Optim..

[42]  C. Jansson.  Guaranteed Accuracy for Conic Programming Problems in Vector Lattices , 2007, 0707.4366.

[43]  Makoto Yamashita,et al.  A high-performance software package for semidefinite programs: SDPA 7 , 2010 .

[44]  Masakazu Muramatsu,et al.  Strange behaviors of interior-point methods for solving semidefinite programming problems in polynomial optimization , 2012, Comput. Optim. Appl..

[45]  Martin Skutella,et al.  Convex quadratic and semidefinite programming relaxations in scheduling , 2001, JACM.

[46]  Jos F. Sturm,et al.  A Matlab toolbox for optimization over symmetric cones , 1999 .

[47]  Masakazu Muramatsu,et al.  Facial Reduction Algorithms for Conic Optimization Problems , 2012, Journal of Optimization Theory and Applications.

[48]  Knud D. Andersen,et al.  Computation of collapse states with von Mises type yield condition , 1998 .

[49]  Arthur T. Benjamin.  Sensible Rules for Remembering Duals - the S-O-B Method , 1995, SIAM Rev..