Maple code of gamma algorithm for global optimization of uncertain functions over compact robust sets

• Published in: Computers & mathematics with applications (1987) Vol. 56; no. 1; pp. 90 - 103
• Main Authors: Delgado Pineda, M., Galperin, E.A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2008
• Subjects: Algorithms; Economics; Gamma algorithm; Mathematical analysis; Mathematical models; Modular; Nonconvex global optimization of uncertain functions; Numerical methods; Optimization; Planes; Uncertainty; Gamma algorithm; Nonconvex global optimization of uncertain functions; Numerical methods
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2007.11.036

Problems with uncertainties are ubiquitous in many areas of science and technology. Due to imprecision of measurements (Heisenberg’s relation), such problems are normal in nuclear physics. Due to fluidity of media, ships at sea and planes in the air have to deal with instability of the currents they move in. Yields in agriculture depend on the whims of weather. Due to the lack of information in economy and finance, problems with uncertainties (stock prices, marketing problems, inflation, unemployment) are commonplace. In such situations, it is necessary to make a choice of better parameters that produce finite intervals of possible values of a given uncertain function at each point of the parameter space. The gamma algorithm [E.A. Galperin, Global optimization in problems with uncertainties, Journal of Nonlinear Analysis 47 (2001) 941–952; E.A. Galperin, Global optimization in problems with uncertainties. The gamma algorithm. Computer and Mathematics with Applications 44 (2002) 853–862] presents a method to make that choice. A new variant of the gamma algorithm based on the beta algorithm is presented for global optimization of uncertain functions over compact robust sets in R n . The set-monotonic algorithm contains a block for problems with equality constraints, and operates within the unit cube [ 0 , 1 ] n for all problems. On this basis, a MAPLE code of modular structure is developed for full global optimization of functions of n variables. The code does not create ill-conditioned situations. Graphics are included, and the solution set can be visualized in plane projections and sections. The code is ready for engineering applications. The results of numerical experiments are presented, with graphs, to illustrate the use of the code.