Global minimization for problems with multiple local minima

Yuefan Deng, James Glimm, Qiqing Yu, Moshe Eisenberg

Research output: Contribution to journalArticlepeer-review


We present a hybrid method for the minimization of the effective free energy of certain physical systems. The three stages of this method approximate the system interaction potential in three forms: (1) square-well, (2) quadratic, and (3) Lennard-Jones. The first stage uses a geometric method to minimize the free energy, based on a square-well potential. The second stage, assuming the pair interaction is quadratic, gives an analytical form for the minimization. The last stage, introducing more realistic physics, i.e., a Lennard-Jones pair interaction, uses the Monte Carlo method to perform minimization. The first stage is less accurate but much more efficient and eliminates most of the local minima of the free energy from further consideration. The refinement done by the latter steps reduces the error and delivers accurate results.

Original languageEnglish (US)
Pages (from-to)89-90
Number of pages2
JournalApplied Mathematics Letters
Issue number2
StatePublished - Mar 1993

ASJC Scopus subject areas

  • Applied Mathematics


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