A new method was proposed for solving optimization problems with noisy functions, the method is called Successive Regression Approximations (SRA). In optimization practice one often resorts to some kind of approximations. Linear and quadratic polynomials, orthogonal functions, Taylor series are the most frequently applied ones. For noisy functions generally derivatives are not available, so SRA is relying only on the function values.
SRA was tested on several problems, the related computer results were published in a series of papers. These problems include solving a one-dimensional equation, probabilistic constrained and two-stage stochastic programming problems, including large-scale ones, a combined model of Prekopa, quadratic stochastic programming problems. SRA is suitable for solving linear programming problems with random technology matrix, too.
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