santanu.dey@isye.gatech.edu

Office: Groseclose, Rm 443
765 Ferst Dr, Atlanta GA 30332

Phone:+1 (404) 385-7483
Fax:+1 (404) 894-2301

Review of Cutting-planes for Mixed Integer Programming

  1. Overview of Cutting Plane Theory (MIP 2024)

Branch-and-Bound Scheme

  1. Theoretical and computational analysis of sizes of branch-and-bound trees

Cutting Planes from Group Relaxation of MILPs

  1. Introduction to Extreme Inequalities for Group Relaxation
  2. Discontinuous Extreme Inequalities
  3. Some Facets of Two-dimensional Infinite Group Problem
  4. Sequential-Merge Inequalities
  5. Trivial Lifting of Facets from Continuous Group Problem to Mixed Integer Group Problem
  6. Extreme Inequalities of Infinite Group Relaxation from Mixing Inequalities
  7. S-free convex sets and cutting planes

Cutting-Plane Evaluation

  1. Finite Split Rank of Triangle and Quadrilateral Inequalities
  2. Lower Bound on Split Rank of Intersection Cuts
  3. How Good are Sparse Cutting-Planes
  4. Effectiveness of Sparse Cutting-planes for Integer Programs with Sparse Constraint Matrix [video]
  5. Aggregation-based cutting-planes for packing and covering integer programs

Other Classes of Cutting Planes for MILPs

  1. Lifting Cutting Planes using Linear Programming
  2. A Verification Based Method to Generate Cutting Planes for IPs
  3. Cutting-Planes from Two Branch Disjunctions

Primal Heuristics

  1. Using Sparsity to Design Primal Heuristics for MILPs: Two Stories

Mixed Integer Nonlinear Programming

  1. Lagrangian dual with zero duality gap that admits decomposition
  2. Sensitivity analysis for mixed binary quadratic programming
  3. Subset selection with sparse matrices
  4. Convex integer programming model to obtain dual bounds for sparse PCA
  5. Chvátal-Gomory Closure of Strictly Convex Body
  6. Some Properties of Convex Hulls of Integer Points Contained in General Convex Set
  7. Some Representability and Duality Results for Convex Mixed-integer Programs
  8. Integer Quadratic Programming is in NP
  9. Some cut-generating functions for second-order conic set

Quadratically Constrained Quadratic Programming

  1. Aggregation of quadratic inequalities and hidden hyperplane convexity
  2. On obtaining the convex hull of quadratic inequalities via aggregations [video]
  3. Lifting Convex Inequalities for Bilinear Programs
  4. Sparse PSD approximation of the PSD cone [video]
  5. Convexification in Global Optimization - A Tutorial [video 1] [video 2]
  6. Convexification of Substructures in Quadratically Constrained Quadratic Programs
  7. New SOCP relaxation and branching rule for bipartite bilinear programs
  8. Analysis of MILP Techniques for the Pooling Problem [video]
  9. New Formulations and Valid Inequalities for Optimal Power Flow Problem