Extrapolated Proportional-Integral Projected Gradient Method for Conic Optimization

Conic optimization is the minimization of a convex quadratic function subject to conic constraints. We introduce a novel first-order method for conic optimization, named extrapolated proportional-integral projected gradient method (xPIPG) , that automatically detects infeasibility. The iterates of x...

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Bibliographic Details
Published inIEEE control systems letters Vol. 7; pp. 73 - 78
Main Authors Yu, Yue, Elango, Purnanand, Acikmese, Behcet, Topcu, Ufuk
Format Journal Article
LanguageEnglish
Published IEEE 2023
Subjects
Convergence
Extrapolation
Gradient methods
infeasibility detection
Mathematical models
Minimization
Optimization
Optimization algorithms
Symmetric matrices
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ISSN2475-1456
2475-1456
DOI10.1109/LCSYS.2022.3186647

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Summary:Conic optimization is the minimization of a convex quadratic function subject to conic constraints. We introduce a novel first-order method for conic optimization, named extrapolated proportional-integral projected gradient method (xPIPG) , that automatically detects infeasibility. The iterates of xPIPG either asymptotically satisfy a set of primal-dual optimality conditions, or generate a proof of primal or dual infeasibility. We demonstrate the application of xPIPG using benchmark problems in model predictive control. xPIPG outperforms many state-of-the-art conic optimization solvers, especially when solving large-scale problems.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2022.3186647