Optimization over Multi-order Cones

Abstract

In this paper we propose multi-order cone programs (MOCPs) as a new class of convex nonlinear optimization problems that includes linear programs, (convex) quadratic programs second-order cone programs and, more generally, pth-order cone programs as special cases. In MOCPs we minimize a linear objective function over the intersection of an affine set and a product of multi-order cones. We refer to them as deterministic multi-order cone programs (DMCOPs) since data defining them are deterministic. We present the definition of DMOCPs in primal and dual standard forms. Then we introduce two-stage stochastic multi-order cone programs (SMOCPs) (with recourse) to handle uncertainty in data defining DMOCPs and deterministic mixed integer multi-order cone programs (DMIMOCPs) to handle DMOCPs with integer-valued variables. We describe an applicational setting and present DMOCP, SMOCP and DMIMOCP models arising in that setting.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 2011
Accession Number
ADA541523

Entities

People

  • Baha M. Alzalg
  • K. A. Ariyawansa

Organizations

  • Washington State University

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Engineering
  • Inequalities
  • Information Operations
  • Interdisciplinary Science
  • Linear Programming
  • Mathematical Programming
  • Mathematics
  • Military Research
  • Operations Research
  • Optimization
  • Semidefinite Programming
  • Standards
  • Systems Science
  • Uncertainty
  • Universities

Fields of Study

  • Computer science

Readers

  • Operations Research