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DOI: 10.23952/cot.2024.31
Received July 12, 2023; Accepted December 13, 2023; Published online May 18, 2024
Abstract. The purpose of this paper is to present unified algorithms to optimally solve real and complex rank-r linear equations corrupted by measurement noise, say e, where part of its elements are outliers, i.e., they appear to be uniquely different from the rest of its elements. Specifically, we show how to obtain an optimal robust sparse solution for underdetermined as well as overdetermined real and complex linear equations, where in both cases we similarly take care of sparsity issues. After removing sparsity issues, we convert robust optimization problems in the complex case to their real counterpart and in both the real and complex cases we arrive at similar real problems. In the complex case instead of solving for the complex unknown vector, we solve for both its real and imaginary vectors.
How to Cite this Article:
D. Hertz, Optimal robust sparse solutions for linear equations via mixed linear (fractional) programming and rank study of complex matrices and their real counterpart, Commun. Optim. Theory 2024 (2024) 31.