Scholarlink

<p>For a function of bounded variation <i>f</i> in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2025_449_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>, we consider the optimization problem of affine total variation, subject to a constraint on the LYZ body <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40304_2025_449_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(\langle f\rangle \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">⟨</mo> <mi>f</mi> <mo stretchy="false">⟩</mo> </mrow> </math></EquationSource> </InlineEquation> under affine transformations, along with its dual problem. As applications, we also derive properties of the solutions to the related optimization problem, as well as properties of the LYZ body.</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

The Optimization Problem for Functions of Bounded Variation

  • 期刊论文

  • 发表日期：

    2025年5月23日

查看全文
  • Wan Li,
  • Shuang Mou,
  • Baocheng Zhu

摘要

For a function of bounded variation f in \(\mathbb {R}^n\) R n , we consider the optimization problem of affine total variation, subject to a constraint on the LYZ body \(\langle f\rangle \) ⟨ f ⟩ under affine transformations, along with its dual problem. As applications, we also derive properties of the solutions to the related optimization problem, as well as properties of the LYZ body.