Efficient Serial and Parallel Implementations of the Cutting Angle Method
We examine efficient computer implementation of one method of deterministic global optimization, the cutting angle method. In this method the objective function is approximated from below with piecewise linear auxiliary functions. The sequence of global minima of these auxiliary functions converges to the global minimum of the objective function. Computing the minima of the auxiliary function is a combinatorial problem, and we show that it can be effectively parallelized. We discuss the improvements made to the serial implementation of the cutting angle method, and ways of distributing computations across multiple processors on parallel and cluster computers.
Keywordsglobal optimization cutting angle method parallel computing
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- A. Bagirov, Derivative-free methods for unconstrained nonsmooth optimization and its numerical analysis, Journal Investigacao Operational, vol. 19 (1999), pp. 75–93.Google Scholar
- A. M. Bagirov and A. M. Rubinov, Cutting angle method and a local search, Journal of Global Optimization, to appear.Google Scholar
- L. M. Batten and G. Beliakov, Fast algorithm for the cutting angle method of global optimization, Journal of Global Optimization, to appear.Google Scholar
- I.M. Bomze and E. de Klerk, Solving standard quadratic optimization problems via linear, semidefinite and copositive programming. Journal of Global Optimization, to appear.Google Scholar
- C. A. Floudas, Deterministic global optimization: theory,methods,and applications, Kluwer Academic Publishers, Dordrecht, 2000.Google Scholar
- R. Horst and H. Tuy, Global optimization: deterministic approaches, Springer-Verlag, Berlin; New York, 1993.Google Scholar
- J. L. Kiepeis, M. G. Ierapetritou and C. A. Floudas, Protein Folding and Peptide Docking - a Molecular Modeling and Global Optimization Approach, Computers and Chemical Engineering, vol. 22 (1998), pp. S 3–S 10.Google Scholar
- F. T. Leighton, Introduction to parallel algorithms and architectures: arrays,trees,hypercubes, M. Kaufmann Publishers, San Mateo, Calif., 1992.Google Scholar
- H. S. Morse,Practical parallel computing, AP Professional, Boston, 1994.Google Scholar
- B. Wilkinson and C. M. Allen, Parallel programming: techniques and applications using networked workstations and parallel computers, Prentice Hall, Upper Saddle River, N.J., 1999.Google Scholar