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- W4308482030 abstract "We propose a simple projection and rescaling algorithm that finds maximum support solutions to the pair of feasibility problems [ text{find} ; xin Lcapmathbb{R}^n_{+} ;;;; text{ and } ; ;;;; text{find} ; hat xin L^perpcapmathbb{R}^n_{+}, ] where $L$ is a linear subspace of $mathbb{R}^n$ and $L^perp$ is its orthogonal complement. The algorithm complements a basic procedure that involves only projections onto $L$ and $L^perp$ with a periodic rescaling step. The number of rescaling steps and thus overall computational work performed by the algorithm are bounded above in terms of a condition measure of the above pair of problems. Our algorithm is a natural but significant extension of a previous projection and rescaling algorithm that finds a solution to the problem [ text{find} ; xin Lcapmathbb{R}^n_{++} ] when this problem is feasible. As a byproduct of our new developments, we obtain a sharper analysis of the projection and rescaling algorithm in the latter special case." @default.
- W4308482030 created "2022-11-12" @default.
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- W4308482030 date "2020-03-19" @default.
- W4308482030 modified "2023-09-26" @default.
- W4308482030 title "Projection and rescaling algorithm for finding maximum support solutions to polyhedral conic systems" @default.
- W4308482030 doi "https://doi.org/10.48550/arxiv.2003.08911" @default.
- W4308482030 hasPublicationYear "2020" @default.
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