Many derivative-free methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penalty-like strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated...

We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the algorithm output is established alongside desirable features of the model-based trust-region subpr...

In this paper we consider nonlinear constrained optimization problems in case where the first order derivatives of the objective function and the constraints can not be used. Up to date only a few approaches have been proposed for tackling such a class of problems. In this work we propose a new algorithm. The starting point of the proposed approach is the possibility to transform the original c...

The filter method is a technique for solving nonlinear programming problems. The filter algorithm has two phases in each iteration. The first one reduces a measure of infeasibility, while in the second the objective function value is reduced. In real optimization problems, usually the objective function is not differentiable or its derivatives are unknown. In these cases it becomes essential to...

Derivative-free optimization has shown advantage in solving sophisticated problems such as policy search, when the environment is noise-free. Many real-world environments are noisy, where solution evaluations are inaccurate due to the noise. Noisy evaluation can badly injure derivative-free optimization, as it may make a worse solution looks better. Sampling is a straightforward way to reduce n...

Derivative-free algorithms are frequently required for the optimization of nonsmooth functions defined by physical experiments or by averaging of the statistics of numerical simulations of chaotic systems such as turbulent flows. The core idea of all efficient algorithms for problems of this class is to keep function evaluations far apart until convergence is approached. Generalized Pattern Sea...

This paper presents an output feedback adaptive control architecture for continuoustime uncertain dynamical systems based on state observer and derivative-free delayed weight update law. The assumption of constant unknown ideal weights is generalized to the existence of time-varying weights without assuming the existence of their derivatives in a time interval. As a result, this approach is par...

A variety of optimization problems associated with oil production involve cost functions and constraints that require calls to a subsurface flow simulator. In many situations gradient information cannot be obtained efficiently, or a global search is required. This motivates the use of derivative-free (non-invasive, blackbox) optimization methods. This chapter describes the use of several deriva...

— In this paper, the performances of the quasi-Newton BFGS algorithm, the NEWUOA derivative free optimizer, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), the Differential Evolution (DE) algorithm and Particle Swarm Optimizers (PSO) are compared experimentally on benchmark functions reflecting important challenges encountered in real-world optimization problems. Dependence of the...

Column generation is a basic tool for the solution of largescale mathematical programming problems. We present a class of column generation algorithms in which the columns are generated by derivative free algorithms, like population-based algorithms. This class can be viewed as a framework to define hybridization of free derivative algorithms. This framework has been illustrated in this article...