Global Optimization

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Global optimization problems consider the problem of finding a global solution that minimizes an objective function. A local minimum is a point at which the objective function value is less than or equal to the value at nearby points but may be larger than the value at a distant point. A global minimum is a point at which the objective function value is less than or equal to the value at all other feasible points. In general, global optimization is more difficult than local optimization. In the special case of convex programming problems, however, all local solutions are also global solutions.

Online Resources

Software Resources

The NEOS Server offers a number of Global Optimization solvers. Other software for Global Optimization includes the following (listed in alphabetical order):

  • cGOP is available from the Computer-Aided Systems Laboratory at Princeton University. It implements a primal-dual decomposition algorithm applicable to general constrained biconvex problems using a set of C subroutines to solve these problems via decomposition and branch-and-bound techniques.
  • LGO (Lipschitz Global Optimizer) integrates several global and local optimization solvers. It does not require derivative information. The product is available for a number of optimization modeling environments and scientific computing platforms.
  • The Mathematica packages MathOptimizer and Global Optimization are applicable to a variety of problems.
  • MCS (Multilevel Coordinate Search) is a MATLAB program for bound constrained global optimization using function values only, based on a multilevel coordinate search that balances global and local search.
  • NLopt is a free/open-source library developed at MIT for nonlinear optimization. It provides a common interface for some (global and local) optimization routines available online as well as original implementations of other algorithms.
  • TOMLAB /CGO is a Matlab toolbox for solving global non-convex (integer) optimization problems where the function is computationally expensive to compute. It offers a choice of three solvers.

References

Textbooks and Published Papers

  • Floudas, C. A. and C. E. Gounaris. 2009. A review of recent advances in global optimization. Journal of Global Optimization 45(1): 3 - 38.
  • Horst, R., P. M. Pardalos, and N. V. Thoai. 2000. Introduction to Global Optimization, 2nd ed. Kluwer Academic Publishers, Dordrecht, The Netherlands.

Journals and Technical Reports

Last updated November 5, 2013