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Cutting Planes for Mixed Integer Linear Programming

  • Merve Bodur, Alberto Del Pia, Santanu S. Dey, Marco Molinaro, "Lower bounds on the lattice-free rank for packing and covering integer programs". [pdf]
  • Merve Bodur, Alberto Del Pia, Santanu S. Dey, Marco Molinaro, Sebastian Pokutta, "Aggregation-based cutting-planes for packing and covering integer programs," Accepted for publication in Mathematical Programming. [doi] [pdf] [slides]
  • Amitabh Basu, Santanu S. Dey, Joseph Paat, "How to choose what you lift". [pdf]
  • Santanu S. Dey, Marco Molinaro, Qianyi Wang, "Analysis of Sparse Cutting-plane for Sparse IPs with Applications to Stochastic IPs," Accepted for publication in Mathematics of Operations Research. [doi] [pdf] [slides] [video]
  • Santanu S. Dey, Andres Iroume, Marco Molinaro, "Some lower bounds on sparse outer approximations of polytopes," Operations Research Letters, 43, 323-328, 2015. [doi] [pdf]
  • Santanu S. Dey, Marco Molinaro, Qianyi Wang, "Approximating Polyhedra with Sparse Inequalities," Mathematical Programming, 154, 329-352, 2015. [doi] [pdf] [slides]
    • [IPCO version] Santanu S. Dey, Marco Molinaro, Qianyi Wang, "How Good are Sparse Cutting-Planes?" 17th Conference on Integer Programming and Combinatorial Optimization , 261-272, 2014. [doi][pdf]
  • Santanu S. Dey, Sebastian Pokutta, "Design and Verify: A New Scheme for Generating Cutting-Planes," Mathematical Programming A, 145, 199-222, 2014. [doi] [pdf] [slides]
    • [IPCO version] Santanu S. Dey, Sebastian Pokutta, “Design and Verify: A New Scheme for Generating Cutting-Planes,” Proceeding 15th Conference on Integer Programming and Combinatorial Optimization, 143 - 155, 2011. [doi] [pdf]
  • Sanjeeb Dash, Santanu S. Dey, Oktay Günlük, “Two Dimensional Lattice-free Cuts and Asymmetric Disjunctions for Mixed-integer Polyhedra,” Mathematical Programming A, 135, 221-254, 2012. [doi] [pdf] [slides]
  • Sanjeeb Dash, Santanu S. Dey, Oktay Günlük. “On Mixed-integer Sets with Two Integer Variables,” Operations Research Letters 39, 305-309, 2011. [doi] [pdf]
  • Santanu S. Dey, Quentin Louveaux, “Split Rank of Triangle and Quadrilateral inequalities,” Mathematics of Operations Research, 36, 432-461, 2011. [doi] [pdf] [slides]
  • Santanu S. Dey, “A Note on Split Rank of Intersection Cuts,” Mathematical Programming A, 130, 107- 124, 2011. [doi] [pdf] [slides]
  • Santanu S. Dey, Laurence A. Wolsey, “Constrained Infinite Group Relaxation of MIPs,” SIAM Journal on Optimization, 20, 2890-2912, 2010. [doi] [pdf] [slides]
  • Santanu S. Dey, Laurence A. Wolsey, “Composite Lifting of Group Inequalities and an Application to Two-Row Mixing Inequalities,” Discrete Optimization, 7, 256-268, 2010. [doi] [pdf] [slides]
  • Santanu S. Dey, Laurence A. Wolsey, “Two Row Mixed Integer Cuts Via Lifting,” Mathematical Programming B, 124, 143-174, 2010. [doi] [pdf] [slides]
    • [IPCO version] Santanu S. Dey, Laurence A. Wolsey, “Lifting integer variables in minimal inequalities corresponding to lattice-free triangles,” Proceeding 13th Conference on Integer Programming and Combinatorial Optimization, 463- 475, 2008. [doi]
  • Santanu S. Dey, Jean-Philippe P. Richard, “Relations between facets of low- and high-dimensional group problems,” Mathematical Programming A, 123, 285-313, 2010. [doi] [pdf] [slides]
    • [IPCO version] Santanu S. Dey, Jean-Philippe P. Richard, “Sequential-Merge facets for two-dimensional group problems,” Proceeding 12th Conference on Integer Programming and Combinatorial Optimization, 30- 42, 2007. [doi]
  • Santanu S. Dey, Jean-Philippe P. Richard, Yanjun Li, Lisa A. Miller, “On Extreme Inequalities for Infinite Group Problems,” Mathematical Programming A, 121, 145- 170, 2010. [doi] [pdf] [slides]
  • Santanu S. Dey, Andrea Lodi, Laurence A. Wolsey, Andrea Tramontani, “On the Practical Strength of Two-Row Tableau Cuts,” INFORMS Journal on Computing , 26, 222-237, 2014. [doi] [pdf]
    • [IPCO version] Santanu S. Dey, Andrea Lodi, Laurence A. Wolsey, Andrea Tramontani, “Experiments with Two Row Tableau Cuts,” Proceeding 14th Conference on Integer Programming and Combinatorial Optimization, 424-437, 2010. [doi]
  • Santanu S. Dey, Jean-Philippe P. Richard, “Linear-Programming-Based Lifting and Its Application to Primal Cutting-Plane Algorithms,” INFORMS Journal on Computing, 21, 137- 150, 2009. [doi] [pdf] [slides]
  • [Review article] Santanu S. Dey, Andrea Tramontani, “Recent Developments in Multiple Row Cuts,” Optima - Mathematical Programming Society Newsletter, 80, 2-8 September 2009. Click here for the Optima Issue.
  • [Book chapter] Jean-Philippe P. Richard, Santanu S. Dey, “The Group-Theoretic Approach in Mixed Integer Programming: Theory, Computation and Perspectives,” Fifty years of Integer Programming 1958-2008: From early years to the state-of-the-art (M. Juenger, T. Liebling, D. Naddef, G. Nemhauser, W. Pulleyblank, G. Reinelt, G. Rinaldi, and L. Wolsey (eds.)), December 2009 (Springer). [doi]
  • Santanu S. Dey, Jean-Philippe P. Richard, “Facets of Two-Dimensional Infinite Group Problems,” Mathematics of Operations Research, 33, 140-166, 2008. [doi] [pdf] [slides]
    • Mixed Integer Non-linear Programming

      • Asteroide Santana, Santanu S. Dey, "Some cut-generating functions for second-order conic sets," Discrete Optimization, 24, 51-65, 2017. [doi] [pdf] [slides]
      • Burak Kocuk, Santanu S. Dey, X. Andy Sun, "New Formulation and Strong MISOCP Relaxations for AC Optimal Transmission Switching Problem," Accepted for publication in IEEE Transactions on Power Systems. [doi] [pdf]
      • Alberto Del Pia, Santanu S. Dey, Marco Molinaro, "Mixed-integer Quadratic Programming is in NP," Mathematical Programming, 162, 225-240, 2017. [doi] [pdf] [slides]
      • Diego A. Morán R., Santanu S. Dey, "Closedness of Integer Hulls of Simple Conic Sets," SIAM Journal on Discrete Mathematics, 30, 70-99, 2016. [doi] [pdf]
        • [IPCO version] Diego A. Morán R., Santanu S. Dey, "A Polynomial-time Algorithm to Check Closedness of Simple Second Order Mixed-integer Sets," Proceeding 16th Conference on Integer Programming and Combinatorial Optimization ,266-277 ,2013. [doi]
      • Daniel Dadush, Santanu S. Dey, Juan Pablo Vielma, "On the Chvátal-Gomory Closure of a Compact Convex Set," Mathematical Programming A, 145, 327-348, 2014. [doi] [pdf]
        • [IPCO version] Daniel Dadush, Santanu S. Dey, Juan Pablo Vielma, “On the Chvátal-Gomory Closure of a Compact Convex Set,” Proceeding 15th Conference on Integer Programming and Combinatorial Optimization, 2011. [doi]
      • Santanu S. Dey, Diego A. Morán R., "Some Properties of Convex Hulls of Integer Points Contained in General Convex Sets," Mathematical Programming A, 141, 507-526, 2013. [doi] [pdf] [slides]
      • Diego A. Morán R., Santanu S. Dey, Juan Pablo Vielma, "A Strong Dual for Conic Mixed-Integer Programs," SIAM Journal on Optimization, 22, 1136-1150, 2012. [doi] [pdf] [slides]
      • Daniel Dadush, Santanu S. Dey, Juan Pablo Vielma, “The Chvátal-Gomory Closure of a Strictly Convex Body,” Mathematics of Operations Research, 36, 227-239, 2011. [doi] [pdf] [slides]
        • [IPCO version] Santanu S. Dey, Juan Pablo Vielma, “The Chvátal-Gomory Closure of an Ellipsoid is a Polyhedron,” Proceeding 14th Conference on Integer Programming and Combinatorial Optimization, 327- 340, 2010. [doi]
      • Daniel Dadush, Santanu S. Dey, Juan Pablo Vielma, “The Split Closure of a Strictly Convex Body,” Operations Research Letters, 39, 121- 126, 2011. [doi] [pdf]
      • Diego A. Morán R., Santanu S. Dey, “On Maximal S-free Convex Sets,” SIAM Journal on Discrete Mathematics, 25, 379-393, 2011. [doi] [pdf]

      0/1 IPs and Related Problems

      • Santanu S. Dey, Andres Iroume, Marco Molinaro, Domenico Salvagnin, "Improving the Randomization Step in Feasibility Pump". [pdf] [slides] [instances]
      • Joey Huchette, Santanu S. Dey, Juan Pablo Vielma, "Beating the SDP bound for the floor layout problem: A simple combinatorial idea," Accepted for publication in INFOR: Information Systems and Operational Research. [doi] [pdf]
      • Joey Huchette, Santanu S. Dey, Juan Pablo Vielma, "Strong mixed-integer formulations for the floor layout problem," Accepted for publication in INFOR: Information Systems and Operational Research [doi] [pdf]
      • Burak Kocuk, Hyemin Jeon, Santanu S. Dey, Jeff Linderoth, James Luedtke, X. Andy Sun, "A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching," Operations Research, 64, 922-938, 2016. [doi] [pdf] [instances]
      • Pelin Damci-Kurt, Santanu S. Dey, Simge Kucukyavuz, "On the Transportation Problem with Market Choice," Discrete Applied Mathematics, 181, 54-77, 2015. [doi] [pdf]
      • Gustavo Angulo, Shabbir Ahmed, Santanu S. Dey, "Improving the integer L-shaped method," INFORMS Journal on Computing, 28, 483-499, 2016. [doi] [pdf]
      • Gustavo Angulo, Shabbir Ahmed, Santanu S. Dey, Volker Kaibel, "Forbidden Vertices," Mathematics of Operations Research, 40, 350-360, 2015. [doi] [pdf]
      • Gustavo Angulo, Shabbir Ahmed, Santanu S. Dey, "Semi-continuous network flow problems," Mathematical Programming A, 145, 565-599, 2014. [doi] [pdf]

      Quadratically Constrained Quadratic Programs

      • Burak Kocuk, Santanu S. Dey, X. Andy Sun, "Matrix Minor Reformulation and SOCP-based Spatial Branch-and-Cut Method for the AC Optimal Power Flow Problem". [pdf]
      • Natashia Boland, Santanu S. Dey, Thomas Kalinowski, Marco Molinaro, Fabian Rigterink, "Bounding the gap between the McCormick relaxation and the convex hull for bilinear functions," Mathematical Programming, 162, 523-535, 2017. [doi] [pdf]
      • Burak Kocuk, Santanu S. Dey, X. Andy Sun, "Strong SOCP relaxations for the optimal power flow problem," Operations Research, 64, 1177-1196, 2016. [doi] [pdf] [slides]
      • Burak Kocuk, Santanu S. Dey, X. Andy Sun, "Inexactness of SDP Relaxation for Optimal Power Flow over Radial Networks and Valid Inequalities for Global Optimization," IEEE Transactions on Power Systems, 31, 642-651, 2016. [doi] [pdf] [instances]
      • Santanu S. Dey, Akshay Gupte, "Analysis Of MILP Techniques For The Pooling Problem" Operations Research, 63, 412-427, 2015. [doi] [pdf] [slides][video][instances]
      • Akshay Gupte, Shabbir Ahmed, Myun Seok Cheon, Santanu S. Dey, "Solving Mixed Integer Bilinear Problems using MIP Formulations," SIAM Journal on Optimization, 23, 721-744, 2013. [doi] [pdf]
      • Akshay Gupte, Shabbir Ahmed, Myun Seok Cheon, Santanu S. Dey, "Relaxations and discretizations for the pooling problem," Journal of Global Optimization, 67, 631-669, 2017. [doi] [pdf]

      Cardinality Constrained Mixed Integer Programs

      • Matthias Walter, Pelin Damci-Kurt, Santanu S. Dey, Simge Kucukyavuz, "On a Cardinality-Constrained Transportation Problem With Market Choice," Operations Research Letters, 44, 170-173, 2016. [doi] [pdf]
      • Feng Qiu, Shabbir Ahmed, Santanu S. Dey, Laurence A. Wolsey, "Covering Linear Programming with Violations," INFORMS Journal on Computing, 26, 531-546, 2014. [doi][pdf]

      Stochastic Programming

      • Kevin Ryan, Shabbir Ahmed, Santanu S. Dey, Deepak Rajan, "Optimization Driven Scenario Grouping". [pdf]
      • Santanu S. Dey, Marco Molinaro, Qianyi Wang, "Analysis of Sparse Cutting-plane for Sparse IPs with Applications to Stochastic IPs". [pdf] [slides] [video]
      • Feng Qiu, Shabbir Ahmed, Santanu S. Dey, "Strengthened Bounds for the Probability of k-Out-Of-n Events," Discrete Applied Mathematics, 198, 232-240, 2016. [doi] [pdf]
      • Gustavo Angulo, Shabbir Ahmed, Santanu S. Dey, "Improving the integer L-shaped method," INFORMS Journal on Computing, 28, 483-499, 2016. [pdf]
      • Feng Qiu, Shabbir Ahmed, Santanu S. Dey, Laurence A. Wolsey, "Covering Linear Programming with Violations," INFORMS Journal on Computing, 26, 531-546, 2014. [doi][pdf]

      Other

      • Efthymios Athanasiou, Santanu S. Dey, Giacomo Valletta, "Groves mechanisms and communication externalities," Review of Economic Design, 20, 1-37, 2016. [doi] [pdf]