Scholarlink

<p>This paper presents a unified framework for constructing smoothing functions tailored to a broad class of widely used regularizers, including the plus function, the pinball function, the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell _0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-norm, the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\ell _p\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation>-norm for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(0 &lt; p \le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>p</mi> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, the MCP, and the SCAD. By transforming nonsmooth regularizers into smooth approximations, the proposed framework facilitates the application of efficient optimization algorithms to sparse optimization problems. The framework is systematically derived from continuous approximations of the step function, offering a principled approach to generating smoothing functions across various regularizers. These approximations are, in turn, constructed using polynomial functions and the Dirac delta function.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Smoothing Functions for Sparse Optimization: A Unified Framework

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月7日

查看全文
  • Chieu Thanh Nguyen,
  • Jein-Shan Chen

摘要

This paper presents a unified framework for constructing smoothing functions tailored to a broad class of widely used regularizers, including the plus function, the pinball function, the \(\ell _0\) ℓ 0 -norm, the \(\ell _p\) ℓ p -norm for \(0 < p \le 1\) 0 < p ≤ 1 , the MCP, and the SCAD. By transforming nonsmooth regularizers into smooth approximations, the proposed framework facilitates the application of efficient optimization algorithms to sparse optimization problems. The framework is systematically derived from continuous approximations of the step function, offering a principled approach to generating smoothing functions across various regularizers. These approximations are, in turn, constructed using polynomial functions and the Dirac delta function.