Abstract
A method of nonlinear optimization is presented. The method is based on searches along weighted random directions together with spline and Lagrangian approximations. We define the concept of mutually dual vectors with respect to the product of two diagonal matrices. These vectors are search directions with orthogonality properties. The properties of the method are analysed for the quadratic case, and an estimate of the minimum from an iterative improvement factor is given. The algorithm has been extensively tested on standard test functions.
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