Benchmark Dataset: Distributed Quadratic Programs (DQP)

Overview

This dataset contains 7,400 randomly generated distributed quadratic program (DQP) instances for benchmarking algorithms for distributed convex optimization via dual decomposition.

Problem Formulation

Each instance is a constraint-coupled quadratic program of the form:

min sum_i=1^N_s (1/2) x_i^T H_i x_i + c_i^T x_i
x_1,...,x_N_s

s.t. sum_i=1^N_s A_i x_i = 0
 x_i^lb <= x_i <= x_i^ub, for all i

where:

• N_s is the number of subsystems
• x_i is the local decision variable of subsystem i
• H_i is a positive-definite cost matrix
• c_i is a cost vector
• A_i is the coupling matrix of subsystem i
• Box constraints: [x_i^lb]_l = -10, [x_i^ub]_l = 10 for all components l

Parameter Generation

A positive entry in A_i indicates that subsystem i produces the corresponding resource; a negative entry indicates consumption.

Dataset Structure

The number of subsystems and coupling constraints were varied systematically to cover a wide range of problem sizes. The benchmark comprises 7,400 instances in total.