Numerical approaches for linear-quadratic optimization with geometric constraints

Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control, and decision-making. This talk will consider an enlarged problem class that also covers logical conditions and cardinality constraints, among others. In particular, we focus on 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 solver-agnostic subproblem reformulations that exploit the problem structure. While convergence guarantees follow from the former, the proposed reformulations lead to significant improvements in computational performance.

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