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Unified smoothing functions for absolute value equation associated with second-order cone

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Abstract In this paper, we explore a unified way to construct smoothing functions for solving the absolute value equation associated with second-order cone (SOCAVE). Numerical comparisons are presented, which illustrate… Click to show full abstract

Abstract In this paper, we explore a unified way to construct smoothing functions for solving the absolute value equation associated with second-order cone (SOCAVE). Numerical comparisons are presented, which illustrate what kinds of smoothing functions work well along with the smoothing Newton algorithm. In particular, the numerical experiments show that the well known loss function widely used in engineering community is the worst one among the constructed smoothing functions, which indicates that the other proposed smoothing functions can be employed for solving engineering problems.

Keywords: smoothing functions; associated second; value equation; equation associated; absolute value; second order

Journal Title: Applied Numerical Mathematics
Year Published: 2019

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