DOI: 10.5281/zenodo.18098478
title: Test instances of disjointly constrained bilinear program

description: BLP SECTION

This section contains the algorithms and benchmark instances for the disjointly constrained bilinear programs.

Algorithms

- PEA: This code implements the Polyhedra Expansion Algorithm(PEA). It solves the disjoint bilinear program using an iterative exploration of optimality polyhedrons. PEA treats the y variables as free and does not require bounds on them.

- Gurobi_Module: Python code that solves the BLP problems using the Gurobi Optimizer as a nonconvex optimization problem. A lower bound on the y variables is required for Gurobi to run.

Instances: The BLP instances are stored inside BLP.zip. They consist of 160 benchmark problems organized into 16 folders numbered 1 through 16. Each folder contains the following for every instance:

An input file containing the full problem specificationas follows:

Line 1: m = number of constraints in the x variables; Line 2: n = number of x variables; Line 3: p = number of y variables; Line 4: l = number of constraints in the y variables

The next line contains the vector c. It has n entries separated by commas. This corresponds to the linear term c^T x.

The next line contains the vector d. It has p entries separated by commas. This corresponds to the linear term d^T y.

The next block contains the matrix Q. It is an n by p matrix written row by row. This defines the bilinear term x^T Q y.

The next block contains the matrix A. It is an m by n matrix that defines the constraints A x = b.

The next block contains the matrix E. It is an l by p matrix that defines the constraints E y >= f.

The next line contains the vector b. It has m entries.

The next line contains the vector f. It has l entries.

The final line contains a lower bound for all y variables. This bound is used only when solving with Gurobi. It is not used by PEA, since PEA treats y as a free variable. The bound was added because Gurobi cannot solve these instances without at least one finite bound on the y variables.

This ordering is the same for all instance files.

An info file containing metadata about the instance. This includes the number of Kernel Problem 1 and Kernel Problem 2 components, the class selections for KP 1, the number of KP 1 problems in each class, the number of local minima, the number of global minima, and lists of global optimal points before and after transformation.

 

BIMATRIX SECTION

This section contains the algorithms and instances for the bimatrix game problems.

- PEA_BMX: Python code implementing the PEA algorithm for bimatrix games. 

- R4B_BMX: Python version of R4B_linear.m of Zhen et al.(2021), customized to solve bimatrix instances.

- Bimatrix instances: The bimatrix game instances are provided in text format. These instances were originally created by Zhen et al. (2021) in MATLAB data format as part of their work in Zhen et al. (2022). Only the payoff matrices are used in PEA_BMX and R4B_BMX. (Note that x_LH and y_LH do not appear to represent the actual solutions, contrary to the description in the original dataset.)

 

REQUIREMENTS

Python 3 NumPy Gurobi and the Gurobi Python interface. Any additional packages are listed in the code headers