Handling of constraints in multiobjective blackbox optimization

This work proposes the integration of two new constraint-handling approaches into the blackbox constrained multiobjective optimization algorithm DMulti-MADS, an extension of the Mesh Adaptive Direct Search (MADS) algorithm for single-objective constrained optimization. The constraints are aggregated into a single constraint violation function which is used either in a two-phase approach, where research of a feasible … Read more

Exploiting Prior Function Evaluations in Derivative-Free Optimization

A derivative-free optimization (DFO) algorithm is presented. The distinguishing feature of the algorithm is that it allows for the use of function values that have been made available through prior runs of a DFO algorithm for solving prior related optimization problems. Applications in which sequences of related optimization problems are solved such that the proposed … Read more

Stochastic trust-region and direct-search methods: A weak tail bound condition and reduced sample sizing

Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple stochastic direct-search and trust-region methods for the optimization of a potentially non-smooth function whose values can only be estimated via stochastic … Read more

Retraction based Direct Search Methods for Derivative Free Riemannian Optimization

Direct search methods represent a robust and reliable class of algorithms for solving black-box optimization problems. In this paper, we explore the application of those strategies to Riemannian optimization, wherein minimization is to be performed with respect to variables restricted to lie on a manifold. More specifically, we consider classic and line search extrapolated variants … Read more

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