2025/10/20 by Alberto De Marchi, De Marchi, Alberto
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2510.17465
openalex publication_date 2025/10/20 · openalex created_date 2025/10/22 · openalex updated_date 2026/07/28
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and cardinality constraints, among others. In particular, we cover also situations where parts of the constraints are nonconvex and possibly complicated, but it is practical to compute projections onto this nonconvex set. Our approach combines the augmented Lagrangian framework with a solver-agnostic structure-exploiting subproblem reformulation. While convergence guarantees follow from the former, the proposed condensing technique leads to significant improvements in computational performance.