Optimization of dual response systems: A comprehensive procedure for degenerate and nondegenerate problems

Enrique Del Castillo, Shu Kai Fan, John Semple

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


Most dual response systems (DRSs) arising in response surface modeling can be approximated using a nonlinear (and typically nonconvex) mathematical program involving two quadratic functions. One of the quadratic functions is used as the objective function, the other for imposing a target constraint. This paper describes an effective heuristic for computing global (or near-global) optimal solutions for this type of problem. The first part of the paper addresses the special case of degeneracy, a condition that makes the system more difficult to solve. Included are means for detecting degeneracy as well as issues relating to its likelihood in practice. The subsequent part of the paper describes our new procedure, AXIS, which rotates a degenerate problem and then decomposes it into a finite sequence of nondegenerate subproblems of lower dimension. The nondegenerate subproblems are solved using the algorithm DRSALG developed earlier. In the final parts of the paper, the AXIS and DRSALG algorithms are integrated into a single dual response solver termed DR2. DR2 is tested against two nonlinear optimization procedures that have been used frequently in dual response applications. The new solver proves to be extremely effective at locating best-practice operating conditions.

Original languageEnglish (US)
Pages (from-to)174-186
Number of pages13
JournalEuropean Journal of Operational Research
Issue number1
StatePublished - Jan 1 1999

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management


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