Proportional-Integral Projected Gradient Method for Infeasibility Detection in Conic Optimization

Understand

A constrained optimization problem is primal infeasible if its constraints cannot be satisfied, and dual infeasible if the constraints of its dual problem cannot be satisfied.

• We propose a novel iterative method, named proportional-integral projected gradient method (PIPG), for detecting primal and dual infeasiblity in convex optimization with quadratic objective function and conic constraints.
• The iterates of PIPG either asymptotically provide a proof of primal or dual infeasibility, or asymptotically satisfy a set of primal-dual optimality conditions.
• Unlike existing methods, PIPG does not compute matrix inverse, which makes it better suited for large-scale and real-time applications.