Universal derivative-free optimization method with quadratic convergence

2011/02/07 by Sergey Moiseev, Moiseev, Sergey
Computer Science · Mathematics · #90C11 #90C26 #90C30 #90C56 #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Matrix Theory and Algorithms #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1102.1347

openalex publication_date 2011/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new universal derivative-free optimization method CDOS (Conjugate Direction with Orthogonal Shift) is proposed. The CDOS method was specially developed to solve optimization tasks where the objective function and constraints are black boxes. The method has quadratic convergence for quadratic and near quadratic functions. An objective function can be non-differentiable and non-continuous. For constrained optimization the constraints can also be non-differentiable and non-continuous. The method handles inequality constraints directly, i.e., it does not transform the objective function, nor uses numeric values of the inequality constraints - it uses only the fact of constraint violation.

Citations

• An efficient method for finding the minimum of a function of several variables without calculating derivatives

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