This note provides a counterexample to a theorem announced in the last part of the paper Analysis of direct searches for discontinuous functions, Mathemati...

A mathematical framework for modelling constrained mixed-variable optimization problems is presented in a blackbox optimization context. The framework intr...

Engineering design is often faced with uncertainties, making it difficult to determine an optimal design. In an unconstrained context, this amounts to choose...

In blackbox optimization, evaluation of the objective and constraint functions is time consuming. In some situations, constraint values may be evaluated in...

A piecewise constant Mayer cost function is used to model optimal control problems in which the state space is partitioned into several regions, each having ...

A small polygon is a polygon of unit diameter. The maximal width of an equilateral small polygon with \(n=2^s\) vertices is not known when \(s \ge 3\). T...

This work is in the context of blackbox optimization where the functions defining the problem are expensive to evaluate and where no derivatives are availabl...

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that sh...

A small polygon is a polygon of unit diameter. The maximal perimeter of a convex equilateral small polygon with \(n=2^s\) vertices is not known when `(s ...

NOMAD is software for optimizing blackbox problems. In continuous development since 2001, it constantly evolved with the integration of new algorithmic...

This paper proposes a way to combine the Mesh Adaptive Direct Search (MADS) algorithm with the Cross-Entropy (CE) method for non smooth constrained optimizat...

This work reviews blackbox optimization applications over the last twenty years, addressed using direct search optimization methods. Emphasis is placed on...

The design of key nonlinear systems often requires the use of expensive blackbox simulations presenting inherent discontinuities whose positions in the varia...

Artificial Intelligence (AI) is the next society transformation builder. Massive AI-based applications include cloud servers, cell phones, cars, and pandemic...

The solution to a biobjective optimization problem is composed of a collection of trade-off solution called the Pareto set. The present work studies the que...

In derivative-free and blackbox optimization, the objective function is often evaluated through the execution of a computer program seen as a blackbox. It ...

This work proposes strategies to handle three types of constraints in the context of blackbox optimization: binary constraints that simply indicate if they a...

This work introduces StoMADS, a stochastic variant of the mesh adaptive direct-search (MADS) algorithm originally developed for deterministic blackbox optim...

In an optimization problem, multiplying an inequality constraint by a positive scalar has no effect on the domain. However, such a transformation might have...

A small polygon is a polygon of unit diameter. The question of finding the largest area of small \(n-\)gons has been answered for some values of \(n\)....