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Loss functions for finite sets

Jiawang Nie () and Suhan Zhong ()
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Jiawang Nie: University of California San Diego
Suhan Zhong: Texas A &M University

Computational Optimization and Applications, 2023, vol. 84, issue 2, No 5, 447 pages

Abstract: Abstract This paper studies loss functions for finite sets. For a given finite set S, we give sum-of-square type loss functions of minimum degree. When S is the vertex set of a standard simplex, we show such loss functions have no spurious minimizers (i.e., every local minimizer is a global one). Up to transformations, we give similar loss functions without spurious minimizers for general finite sets. When S is approximately given by a sample set T, we show how to get loss functions by solving a quadratic optimization problem. Numerical experiments and applications are given to show the efficiency of these loss functions.

Keywords: Loss function; Finite set; Polynomial; Spurious minimizer; Optimization; 90C23; 65K05; 90C30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10589-022-00420-9

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