Projections onto the Set of Feasible Inputs and the Set of Feasible Solutions

TL;DR

This paper investigates methods for projecting onto feasible input and solution sets in polynomial optimization problems to enhance solver robustness, analyzing complexity and formulations with applications to power flow problems.

Contribution

It introduces new approaches for projections in POPs, addressing computational complexity and convexification, with practical applications to power systems.

Findings

Projection methods improve robustness of POP solvers.

Complexity analysis of projection problems in POP.

Application to IEEE power flow test cases.

Abstract

We study the projection onto the set of feasible inputs and the set of feasible solutions of a polynomial optimisation problem (POP). Our motivation is increasing the robustness of solvers for POP: Without a priori guarantees of feasibility of a particular instance, one should like to perform the projection onto the set of feasible inputs prior to running a solver. Without a certificate of optimality, one should like to project the output of the solver onto the set of feasible solutions subsequently. We study the computational complexity, formulations, and convexifications of the projections. Our results are illustrated on IEEE test cases of Alternating Current Optimal Power Flow (ACOPF) problem.