A survey on second-order conditions for nonlinear symmetric cone programming via squared slack variables (New Trends of Numerical Optimization in Advanced Information-Oriented Society)

• Fukuda, Ellen Hidemi

  Graduate School of Informatics, Kyoto University

• Lourenco, Bruno Figueira

  Graduate School of Information Science and Technology, University of Tokyo

• Fukushima, Masao

  Faculty of Science and Engineering, Nanzan University

Bibliographic Information

Other Title

• A survey on second-order conditions for nonlinear symmetric cone programming via squared slack variables

Abstract

The nonlinear symmetric cone programming (NSCP) problems contain as special cases the nonlinear semidefinite programming, the nonlinear second-order cone programming and the nonlinear programming problems. In this survey, we first explain the basics about Euclidean Jordan algebras and symmetric cones. Then, we observe that NSCP problems can be reformulated as nonlinear programming problems with the use of squared slack variables. Using such reformulations, we show how to obtain second-order optimality conditions for NSCP problems. In particular, under the strict complementarity condition, we lead to a description of the so-called sigma-term.

Journal

• RIMS Kokyuroku

  RIMS Kokyuroku 2108 135-143, 2019-04

  京都大学数理解析研究所

Keywords

• Nonlinear symmetric cone programming
• optimality conditions
• second-order conditions
• sigma-term

Details

• CRID: 1050003824810808832
• NII Article ID: 120006861529
• NII Book ID: AN00061013
• ISSN: 18802818
• HANDLE: 2433/251928
• NDL BIB ID: 029814894
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I029814894
• Text Lang: en
• Article Type: departmental bulletin paper
• Data Source:
  • IRDB
  • NDL
  • CiNii Articles