The convex and monotone functions associated with second-order cone

研究成果: 雜誌貢獻期刊論文同行評審

34 引文 斯高帕斯(Scopus)

摘要

Like the matrix-valued functions used in solutions methods for semidefinite programs (SDPs) and semidefinite complementarity problems (SDCPs), the vector-valued functions associated with second-order cones are defined analogously and also used in solutions methods for second-order-cone programs (SOCPs) and second-order-cone complementarity problems (SOCCPs). In this article, we study further about these vector-valued functions associated with second-order cones (SOCs). In particular, we define the so-called SOC-convex and SOC-monotone functions for any given function f: ℝ → ℝ. We discuss the SOC-convexity and SOC-monotonicity for some simple functions, e.g., f(t) = t2, t3 1/t, t1/2, |t|, and [t] +. Some characterizations of SOC-convex and SOC-monotone functions are studied, and some conjectures about the relationship between SOC-convex and SOC-monotone functions are proposed.

原文英語
頁(從 - 到)363-385
頁數23
期刊Optimization
55
發行號4
DOIs
出版狀態已發佈 - 2006 八月 1

ASJC Scopus subject areas

  • 控制和優化
  • 管理科學與經營研究
  • 應用數學

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