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- W4383860767 abstract "Consider the linear equation $mathbf{A}mathbf{x}=mathbf{y}$, where $mathbf{A}$ is a $ktimes N$-matrix, $mathbf{x}inmathcal{K}subset mathbb{R}^N$ and $mathbf{y}inmathbb{R}^M$ a given vector. When $mathcal{K}$ is a convex set and $Mnot= N$ this is a typical ill-posed, linear inverse problem with convex constraints. Here we propose a new way to solve this problem when $mathcal{K} = prod_j[a_j,b_j]$. It consists of regarding $mathbf{A}mathbf{x}=mathbf{y}$ as the constraint of a convex minimization problem, in which the objective (cost) function is the dual of a moment generating function. This leads to a nice minimization problem and some interesting comparison results. More importantly, the method provides a solution that lies in the interior of the constraint set $mathcal{K}$. We also analyze the dependence of the solution on the data and relate it to the Le Chatellier principle." @default.
- W4383860767 created "2023-07-11" @default.
- W4383860767 creator A5026656556 @default.
- W4383860767 date "2023-07-05" @default.
- W4383860767 modified "2023-09-27" @default.
- W4383860767 title "Ill-posed linear inverse problems with box constraints: A new convex optimization approach" @default.
- W4383860767 doi "https://doi.org/10.48550/arxiv.2307.03680" @default.
- W4383860767 hasPublicationYear "2023" @default.
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