Bistable mechanical systems exhibit two stable configurations where the elastic energy is locally minimized. To realize such systems, origami techniques ha...

This work introduces a _partitioned optimization framework_ (POf) to ease the solving process for optimization problems for which fixing some variables to a...

This paper introduces a new step to the Direct Search Method (DSM) to strengthen its convergence analysis. By design, this so-called covering step may e...

This work introduces solar, a collection of ten optimization problem instances for benchmarking blackbox optimization solvers. The instances present differ...

Heterogeneous datasets emerge in various machine learning or optimization applications that feature different data sources, various data types and complex re...

Cellular solids are structures which have applications in mechanical engineering to make lightweight structures and heat exchangers, in biomedical engineer...

The cosine measure was introduced in 2003 to quantify the richness of a finite positive spanning sets of directions in the context of derivative-free direc...

This work introduces a novel multi-fidelity blackbox optimization algorithm designed to alleviate the resource-intensive task of evaluating infeasible points...

This paper addresses risk averse constrained optimization problems where the objective and constraint functions can only be computed by a blackbox subject to...

This work considers stochastic optimization problems in which the objective function values can only be computed by a blackbox corrupted by some random noise...

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 \(n\)....

We are interested in blackbox optimization for which the user is aware of monotonic behaviour of some constraints defining the problem. That is, when incr...

The present work is in a context of derivative-free optimization involving direct search algorithms guided by surrogate models of the original problem. The...

This is a two-part work. In Part I, low-cost and representative reduced-fidelity models of two versions of the HYDROTEL hydrological model are constructed, u...

Dealing with computationally-intensive calibration processes is still common in distributed hydrological modelling despite the computing power growth. Comput...

In the recent years, the development of new algorithms for multiobjective optimization has considerably grown. A large number of performance indicators has...

The parallel space decomposition of the Mesh Adaptive Direct Search algorithm (PSD-MADS proposed in 2008) is an asynchronous parallel method for constrained ...

Derivative-free optimization (DFO) is the mathematical study of the optimization algorithms that do not use derivatives. One branch of DFO focuses on model-...

The mesh adaptive direct search (MADS) algorithm is designed for blackbox optimization problems for which the functions defining the objective and the constr...

We investigate surrogate-assisted strategies for global derivative-free optimization using the mesh adaptive direct search MADS blackbox optimization algorit...

Despite the lack of theoretical and practical convergence support, the Nelder-Mead (NM) algorithm is widely used to solve unconstrained optimization proble...

The calibration of hydrological models is here formulated as a Blackbox optimization problem where the only information available to the optimization algorit...

The Runge-Kutta class of iterative methods is designed to approximate solutions of a system of ordinary differential equations (ODE). The second-order cla...

Locally weighted regression combines the advantages of polynomial regression and kernel smoothing. We present three ideas for appropriate and effective use...

The Mesh Adaptive Direct Search algorithm (MADS) is an iterative method for constrained blackbox optimization problems. One of the optional MADS features i...

Blackbox optimization problems are often contaminated with numerical noise, and direct search methods such as the Mesh Adaptive Direct Search (MADS) algorit...

The authors investigate the complexity needed in the structure of the scenario trees to maximize energy production in a rolling-horizon framework. Three comp...

We present a new derivative-free trust-region (DFTR) algorithm to solve general nonlinear constrained problems with the use of an augmented Lagrangian m...

We study derivative-free constrained optimization problems and propose a trust-region method that builds linear or quadratic models around the best feasible ...

This paper presents an optimization method to solve the short-term unit commitment and loading problem with uncertain inflows. A scenario tree is built base...

The subdifferential of a function is a generalization for nonsmooth functions of the concept of gradient. It is frequently used in variational analysis, part...

The paper shows that among all equilateral polygons with a given number of sides and the same diameter, the regular polygon has the maximal area.

This document describes the NOMAD software, a C++ implementation of the Mesh Adaptive Direct Search (MADS) algorithm designed for constrained optimization of...

In prior works, this group demonstrated the feasibility of valid adaptive sequential designs for crossover bioequivalence studies. In this paper, we extend t...

We study the function returning the sum of the k components of largest magnitude of a vector. We show that if a nonnegative vector x is such that its Eu...

The Mesh Adaptive Direct Search (MADS) algorithm is designed for blackbox optimization problems subject to general inequality constraints. Currently, MADS do...

This paper presents a new method for solving the short-term unit commitment and loading problem of a hydropower system. Dynamic programming is used to comput...

Blackbox optimization deals with situations in which the objective function and constraints are typically computed by launching a time-consuming computer ...

The Mesh Adaptive Direct Search algorithm (MADS) algorithm is designed for nonsmooth blackbox optimization problems in which the evaluation of the funct...

Consider a scale that accepts three marbles of different weights. The scale only ranks the marbles, by indicating the heaviest, the lightest and the middle ...

Blackbox optimization typically arises when the functions defining the objective and constraints of an optimization problem are computed through a computer...

The Mesh Adaptive Direct Search (MADS) class of algorithms is designed for nonsmooth optimization, where the objective function and constraints are typical...

The paper answers an open problem introduced by Bezdek and Fodor in 2000. The width of any unit-diameter octagon is shown to be less than or equal to `(\fra...

This paper presents a framework to determine optimal maintenance planning of a fleet of complex and independent systems. They are made up of several major co...

OPAL is a general-purpose system for modeling and solving algorithm optimization problems. OPAL takes an algorithm as input, and as output it suggests para...

Accurate measurements of snow water equivalent (SWE) is an important factor in managing water resources for hydroelectric power generation. SWE over a catchm...

In the context of algorithmic parameter optimization, there is much room for efficient usage of computational resources. We consider the OPAL framework in wh...

During alloy and process design, it is often desired to identify regions of design or process variables for which certain calculated functions have optimal v...

The present paper describes the coupling of the Mesh Adaptive Direct Search (MADS) algorithm with the FactSage thermochemical software, which allows to calcu...

The paper proposes a framework for sensitivity analyses of blackbox constrained optimization problems for which Lagrange multipliers are not available. Two s...

We propose a new approach to construct adaptive multiscale orthonormal (AMO) bases of R^<i>N</i> that provide highly sparse signal representations....

The paper answers the three distinct questions of maximizing the perimeter, diameter and area of equilateral unit-width convex polygons. The solution to each...

A positive basis is a minimal set of vectors whose nonnegative linear combinations span the entire space R<i>ⁿ</i>. Interest in positive bases wa...

In this paper we establish the definition of the <i>set of &epsilon;-proper equilibria</i> of a bimatrix game. We define a 0-1 mixed quadratic program to ge...

The main goal of this paper is to bring a contribution in order to facilitate automatic refinement of Bimatrix Game Nash extreme equilibria. We show how maxi...

We introduce the OPAL framework in which the identification of good algorithmic parameters is interpreted as a black box optimization problem whose variables...

Recent advances in coupling novel optimization methods to large-scale computing problems have opened the door to tackling a diverse set of physically realist...

Relationships between the diameter of a set of <i>n</i> points in the plane at mutual distance at least one, the diameter of an equilateral <i>n</i>-gon and ...

This work analyzes constrained black box optimization in which the functions defining the problem are periodic with respect to some or all the variables. We ...

This work studies multi-objective optimization <i>(MOP)</i> of nonsmooth functions subject to general constraints. We first present definitions and optimalit...

A recent paper of Tuy and Hoai-Phuong published in <i>JOGO</i> (2007) 37:557--569 observes that there are errors in the reformulation of a signomial geometr...

<p>The class of Mesh Adaptive Direct Search (MADS) algorithms is designed for the optimization of constrained black-box problems. The purpose of this paper i...

A polygon is said to be <i>simple</i> if the only points of the plane belonging to two of its edges are its vertices. We answer the question of finding, ...

The hexagon and heptagon with unit diameter and maximum sum of Euclidean distances between vertices are determined by enumerating diameter configurations, an...

The purpose of this paper is to introduce a new way of choosing directions for the Mesh Adaptive Direct Search (MADS) class of algorithms. The advantages of...

We propose a new approach to solve the multi-objective portfolio selection problem in the presence of skewness. The selection of efficient portfolios require...

In previous work, bimatrix games were expressed as parametric linear mixed 0-1 programs and the <img src="/cgi-bin/mimetex.cgi?{\rm E}_\chi">MIP algorithm w...

Consider a convex polygon <i>V_n</i> with <i>n</i> sides, perimeter <i>P_n</i>, diameter <i>D_n</i>, area <i>A_n</i>...

This paper describes a Parallel Space Decomposition (PSD) technique for the Mesh Adaptive Direct Search (MADS) algorithm. MADS extends Generalized Pattern ...

In previous work, the generalized pattern search (GPS) algorithm for linearly constrained (continuous) optimization was extended to mixed variable problems...

We propose a new algorithm for general constrained derivative-free optimization. As in most methods, constraint violations are aggregated into a single con...

This paper proposes a way to combine the Mesh Adaptive Direct Search (MADS) algorithm, which extends the Generalized Pattern Search (GPS) algorithm, with th...

We consider the problem of separating two sets of points in an n-dimensional real space with a (hyper)plane that minimizes the sum of <i>L</i>₂-n...

This work deals with bound constrained multiobjective optimization (<i>MOP</i>) of nonsmooth functions for problems in which the structure of the objective ...

This paper presents two new results on the enumeration of all extreme equilibria of the sequence form of a two person extensive game. The sequential form of...

In this paper, the general problem of chemical process optimization defined by a computer simulation is formulated. It is generally a nonlinear, non-convex,...

The value <img src="/cgi-bin/mimetex.cgi?\frac{1}{2n} \cot\left( \frac{\pi}{2n}\right)"> is shown to be an upper bound on the width of any <i>n</i>-sided p...

From the pentagon onwards, the area of the regular convex polygon with <i>n</i> sides and unit diameter is greater for each odd number <i>n</i> than for the...

In [<i>SIAM J. Optim.</i>, 17 (2006), pp. 188–217] Audet and Dennis proposed the class of <i>mesh adaptive direct search algorithms</i> (MADS) for minimizat...

This work shows how disjunctive cuts can be generated for a bilevel linear programming problem (<i>BLP</i>) with continuous variables. First, a brief summar...

Consider a convex polygon <i>V_n</i> with <i>n</i> sides, perimeter <i>P_n</i>, diameter <i>D_n</i>, area <i>A_n</i>,...

Quel octogone de diamère unité (ou petit octogone) possède la plus grande surface ou le plus grand périmètre? Serait-ce l'octogone régulier? Eh! non, il n'en...

This paper is intended not as a survey, but as an introduction to some ideas behind the class of mesh adaptive direct search (MADS) methods. Space limitatio...

An alternative definition of the linear bilevel programming problem <i>BLP</i> has recently been proposed by Lu, Shi, and Zhang. This note shows that the pr...

A previous analysis of second-order behavior of pattern search algorithms for unconstrained and linearly constrained minimization is extended to the more gen...

The convex octagon with unit diameter and maximum perimeter is determined. This answers an open question dating from 1922. The proof uses geometric reasonin...

The objectives of this paper are twofold; we first demonstrate the flexibility of the mesh adaptive direct search (MADS) in identifying locally optimal algo...

We consider the problem of separating two sets of points in an <i>n</i>-dimensional real space with a (hyper)plane that minimizes the sum of <i>L<sub>p</sub...

<p> This paper introduces the Mesh Adaptive Direct Search (MADS) class of algorithms for nonlinear optimization. MADS extends the Generalized Pattern Searc...

A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the Audet-De...

Linear mixed 0-1 integer programming problems may be reformulated as equivalent continuous bilevel linear programming (<i>BLP</i>) problems. We exploit the...

Bimatrix and polymatrix games are expressed as parametric linear 0-1 programs. This leads to an algorithm for complete enumeration of their extreme equilibri...

Goal Programming with fractional objectives can be reduced to mathematical programming with a linear objective under linear and quadratic constraints, thus...

This paper answers a query of S. Vincze (Acta Univ. Szeged, Sect. Sci. Math. 12 A (1950) 136-142): find the convex octagon with unit-length sides and minim...

This paper formulates and analyzes a pattern search method for general constrained optimization based on filter methods for step acceptance. Roughly, a f...

Cet article propose un modèle d’optimisation des stratégies de maintenance pour une meilleure intégration dans un plan de production préétabli. Le modèle est...

We present an exact algorithm and three applications of nonconvex quadratically constrained quadratic programming. First, we consider the pooling problem fro...

The convergence theory of generalized pattern search algorithms for unconstrained optimization guarantees under mild conditions that the method produces a li...

The pooling problem, which is fundamental to the petroleum industry, describes a situation where products possessing different attribute qualities are mixed...

A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses th...

This paper describes a method for evaluating the kinetic constants in a rate expression for catalytic combustion applications using experimental light-off c...

This paper contains a new convergence analysis for the Lewis and Torczon GPS class of pattern search methods for linearly constrained optimization. The ana...

Thrackleation of graphs and global optimization for quadratically constrained quadratic programming are used to find the octagon with unit diameter and larg...

In the literature, thermal insulation systems with a fixed number of heat intercepts have been optimized with respect to intercept locations and temperature...

The set of equilibrium points of a bimatrix game is the union of polytopes that are not necessarily disjoint. Knowledge of the vertices of these polytopes ...

We pursue the study of concavity cuts for the disjoint bilinear programming problem. This optimization problem has two equivalent symmetric linear maxmin r...

We present a branch and cut algorithm that yields in finite time, a globally <img src="epsilon.gif" align=bottom>-optimal (with respect to feasibility and o...

We present branch and bound algorithms that enumerate in finite time all Nash equilibria for strategic and sequence form bimatrix games. For each forms, th...

The disjoint bilinear programming problem can be reformulated using two distinct linear maxmin programming problems. There is a simple bijection between the...

The maxmin problem models a game sequentially played by two players having opposite objective. Before making his move, the first player must anticipate the...

We study links between the bilevel linear and linear mixed 0-1 programming problems. A new reformulation of the linear mixed 0-1 programming problem into a...

We present a method to compute valid concavity cuts for the linear maxmin programming problem. We consider a primal and a dual approach. In both cases the p...