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arXiv · 2109.02756

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

Yue Yu·Ufuk Topcu
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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.

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Yue Yu, Ufuk Topcu. 2021-09-11. Proportional-Integral Projected Gradient Method for Infeasibility Detection in Conic Optimization. https://arxiv.org/abs/2109.02756

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