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UV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{a ...

UV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}... In this paper we study optimization problems involving convex nonlinear semidefinite programming (CSDP). Here we convert CSDP into eigenvalue problem by exact penalty function, and apply the U\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\cal U}$$\end{document}-Lagrangian theory to the function of the largest eigenvalues, with matrix-convex valued mappings. We give the first-and second-order derivatives of U\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\cal U}$$\end{document}-Lagrangian in the space of decision variables Rm when transversality condition holds. Moreover, an algorithm frame with superlinear convergence is presented. Finally, we give one application: bilinear matrix inequality (BMI) optimization; meanwhile, list their UV\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\cal U}{\cal V}$$\end{document} decomposition results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

UV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{a ...

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Publisher
Springer Journals
Copyright
Copyright © The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2021
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-021-1037-5
Publisher site
See Article on Publisher Site

Abstract

In this paper we study optimization problems involving convex nonlinear semidefinite programming (CSDP). Here we convert CSDP into eigenvalue problem by exact penalty function, and apply the U\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\cal U}$$\end{document}-Lagrangian theory to the function of the largest eigenvalues, with matrix-convex valued mappings. We give the first-and second-order derivatives of U\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\cal U}$$\end{document}-Lagrangian in the space of decision variables Rm when transversality condition holds. Moreover, an algorithm frame with superlinear convergence is presented. Finally, we give one application: bilinear matrix inequality (BMI) optimization; meanwhile, list their UV\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\cal U}{\cal V}$$\end{document} decomposition results.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Oct 1, 2021

Keywords: semidefinite programming; nonsmooth optimization; eigenvalue optimization; UV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal U}{\cal V}$$\end{document}-decomposition; U\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\cal U}$$\end{document}-Lagrangian; smooth manifold; second-order derivative; 90C30; 52A41; 49J52; 15A18

References