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### Cutting Planes for Mixed Integer Linear Programming

- Santanu S. Dey, Marco Molinaro,"Theoretical challenges towards cutting-plane selection," Accepted for publication in
*Mathematical Programming*. [pdf] - Santanu S. Dey, Andres Iroume, Guanyi Wang, "The Strength of Multi-row Aggregation Cuts for Sign-pattern Integer Programs". [pdf]
- 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,"
*Mathematics of Operations Research*, 43, 304-332, 2018. [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] - 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] - 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]

- [IPCO version] Santanu S. Dey, Laurence A. Wolsey, “Lifting integer variables in minimal inequalities corresponding to lattice-free triangles,” Proceeding 13th Conference on
- 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]

- [IPCO version] Santanu S. Dey, Jean-Philippe P. Richard, “Sequential-Merge facets for two-dimensional group problems,” Proceeding 12th Conference on
- 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]

- [IPCO version] Santanu S. Dey, Andrea Lodi, Laurence A. Wolsey, Andrea Tramontani, “Experiments with Two Row Tableau Cuts,” Proceeding 14th Conference on
- 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] - 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,"
*IEEE Transactions on Power Systems*, 32, 4161-4170, 2017. [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]

- [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
- 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]

- [IPCO version] Daniel Dadush, Santanu S. Dey, Juan Pablo Vielma, “On the Chvátal-Gomory Closure of a Compact Convex Set,” Proceeding 15th Conference on
- 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]

- [IPCO version] Santanu S. Dey, Juan Pablo Vielma, “The Chvátal-Gomory Closure of an Ellipsoid is a Polyhedron,” Proceeding 14th Conference on
- 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] - Santanu S. Dey, Andres Iroume, Marco Molinaro, Domenico Salvagnin, "Improving the Randomization Step in Feasibility Pump,"
*SIAM Journal on Optimization*, 28, 355-378, 2018. [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] - Santanu S. Dey, Asteroide Santana, Yang Wang, "New SOCP relaxation and branching rule for bipartite bilinear programs". [pdf] [slides] [instances]
- 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," Accepted for publication in
*Mathematical Programming C*. [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] - 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] - 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]