Distributed Quadratic Constrained Coupled Systems for Dual Decomposition

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 Parameter Distribution / Method Cost vector c_i i.i.d. entries drawn from N(0, 1) Cost matrix H_i Constructed as N_i^T * N_i where N_i has i.i.d. N(0,1) entries, guaranteeing positive definiteness Coupling matrix A_i Element-wise product B_i ∘ C_i, where B_i is drawn from a continuous uniform distribution and C_i from a discrete uniform distribution 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. Dimension varied Values Number of subsystems N_s Multiple values (small to large) Number of coupling constraints m Multiple values (small to large)