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

Abstract

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. We demonstrate the application of PIPG in quasiconvex and mixed-integer optimization using examples in constrained optimal control.

References in corpus (4)

• On the Asymptotic Behavior of the Douglas-Rachford and Proximal-Point Algorithms for Convex Optimization
• On the Minimal Displacement Vector of the Douglas-Rachford Operator
• The primal-dual hybrid gradient method reduces to a primal method for linearly constrained optimization problems
• Convex Optimization for Trajectory Generation