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Conic optimization is the minimization of a convex quadratic function subjectto conic constraints. We introduce a novel first-order method for conicoptimization, named \emph{extrapolated proportional-integral projected gradientmethod (xPIPG)}, that automatically detects infeasibility. The iterates ofxPIPG either asymptotically satisfy a set of primal-dual optimality conditions,or generate a proof of primal or dual infeasibility. We demonstrate theapplication of xPIPG using benchmark problems in model predictive control.xPIPG outperforms many state-of-the-art conic optimization solvers, especiallywhen solving large-scale problems.

Extrapolated Proportional-Integral Projected Gradient Method for Conic Optimization