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. Subset selection with sparse matrices
  2. Convex integer programming model to obtain dual bounds for sparse PCA
  3. Chvátal-Gomory Closure of Strictly Convex Body
  4. Some Properties of Convex Hulls of Integer Points Contained in General Convex Set
  5. Some Representability and Duality Results for Convex Mixed-integer Programs
  6. Integer Quadratic Programming is in NP
  7. 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