Double well potential function and its optimization in the n-dimensional real space - Part I

Shü Cherng Fang, David Y. Gao, Gang Xüan Lin, Rüey Lin Sheü, Wenxün Xing

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


A special type of multi-variate polynomial of degree 4, called the double well potential function, is studied. It is derived from a discrete approx imation of the generalized Ginzburg-Landau functional, and we are interested in understanding its global minimum solution and all local non-global points. The main difficulty for the model is due to its non-convexity. In Part I of the paper, we first characterize the global minimum solution set, whereas the study for local non-global optimal solutions is left for Part II. We show that, the dual of the Lagrange dual of the double well potential problem is a linearly constrained convex minimization problem, which, under a designated nonlin ear transformation, can be equivalently mapped to a portion of the original double well potential function containing the global minimum. In other words, solving the global minimum of the double well potential function is essentially a convex minimization problem, despite of its non-convex nature. Numerical examples are provided to illustrate the important features of the problem and the mapping in between.

Original languageEnglish
Pages (from-to)1291-1305
Number of pages15
JournalJournal of Industrial and Management Optimization
Issue number3
Publication statusPublished - 2017 Jul 1

All Science Journal Classification (ASJC) codes

  • Business and International Management
  • Strategy and Management
  • Control and Optimization
  • Applied Mathematics


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