Characterizing Set Containments Involving Infinite Convex Constraints and Reverse-Convex Constraints

  • Authors:

  • V. Jeyakumar

  • Affiliations:

  • -

  • Venue:
  • SIAM Journal on Optimization
  • Year:
  • 2002

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Abstract

Dual characterizations of the containment of a closed convex set, defined by infinite convex constraints, in an arbitrary polyhedral set, in a reverse-convex set, defined by convex constraints, and in another convex set, defined by finite convex constraints, are given. A special case of these dual characterizations has played a key role in generating knowledge-based support vector machine classifiers which are powerful tools in data classification and mining. The conditions in these dual characterizations reduce to simple nonasymptotic conditions under Slater's constraint qualification.