Hierarchically constrained blackbox optimization

In blackbox optimization, evaluation of the objective and constraint functions is time consuming. In some situations, constraint values may be evaluated independently or sequentially. The present work proposes and compares two strategies to define a hierarchical ordering of the constraints and to interrupt the evaluation process at a trial point when it is detected that … Read more

Model-Based Derivative-Free Methods for Convex-Constrained Optimization

We present a model-based derivative-free method for optimization subject to general convex constraints, which we assume are unrelaxable and accessed only through a projection operator that is cheap to evaluate. We prove global convergence and a worst-case complexity of $O(\epsilon^{-2})$ iterations and objective evaluations for nonconvex functions, matching results for the unconstrained case. We introduce … Read more

Adaptive Finite-Difference Interval Estimation for Noisy Derivative-Free Optimization

A common approach for minimizing a smooth nonlinear function is to employ finite-difference approximations to the gradient. While this can be easily performed when no error is present within the function evaluations, when the function is noisy, the optimal choice requires information about the noise level and higher-order derivatives of the function, which is often … Read more

Full-low evaluation methods for derivative-free optimization

We propose a new class of rigorous methods for derivative-free optimization with the aim of delivering efficient and robust numerical performance for functions of all types, from smooth to non-smooth, and under different noise regimes. To this end, we have developed Full-Low Evaluation methods, organized around two main types of iterations. The first iteration type … Read more

Derivative-free separable quadratic modeling and cubic regularization for unconstrained optimization

We present a derivative-free separable quadratic modeling and cubic regularization technique for solving smooth unconstrained minimization problems. The derivative-free approach is mainly concerned with building a quadratic model that could be generated by numerical interpolation or using a minimum Frobenious norm approach, when the number of points available does not allow to build a complete … Read more

Quantifying uncertainty with ensembles of surrogates for blackbox optimization

This work is in the context of blackbox optimization where the functions defining the problem are expensive to evaluate and where no derivatives are available. A tried and tested technique is to build surrogates of the objective and the constraints in order to conduct the optimization at a cheaper computational cost. This work proposes different … Read more

NOMAD version 4: Nonlinear optimization with the MADS algorithm

NOMAD is software for optimizing blackbox problems. In continuous development since 2001, it constantly evolved with the integration of new algorithmic features published in scientific publications. These features are motivated by real applications encountered by industrial partners. The latest major release of NOMAD, version 3, dates from 2008. Minor releases are produced as new features … Read more

On the Numerical Performance of Derivative-Free Optimization Methods Based on Finite-Difference Approximations

The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing gradients of a smoothed approximation of the objective function (and constraints), and employing them within established codes. These … Read more

Scalable Subspace Methods for Derivative-Free Nonlinear Least-Squares Optimization

We introduce a general framework for large-scale model-based derivative-free optimization based on iterative minimization within random subspaces. We present a probabilistic worst-case complexity analysis for our method, where in particular we prove high-probability bounds on the number of iterations before a given optimality is achieved. This framework is specialized to nonlinear least-squares problems, with a … Read more

A simulation-based optimization approach for the calibration of a discrete event simulation model of an emergency department

Accurate modeling of the patient flow within an Emergency Department (ED) is required by all studies dealing with the increasing and well-known problem of overcrowding. Since Discrete Event Simulation (DES) models are often adopted with the aim of assessing solutions for reducing the impact of this worldwide phenomenon, an accurate estimation of the service time … Read more