PDFO: A Cross-Platform Package for Powell’s Derivative-Free Optimization Solvers

The late Professor M. J. D. Powell devised five trust-region derivative-free optimization methods, namely COBYLA, UOBYQA, NEWUOA, BOBYQA, and LINCOA. He also carefully implemented them into publicly available solvers, which are renowned for their robustness and efficiency. However, the solvers were implemented in Fortran 77 and hence may not be easily accessible to some users. … Read more

An Optimal Interpolation Set for Model-Based Derivative-Free Optimization Methods

This paper demonstrates the optimality of an interpolation set employed in derivative-free trust-region methods. This set is optimal in the sense that it minimizes the constant of well-poisedness in a ball centred at the starting point. It is chosen as the default initial interpolation set by many derivative-free trust-region methods based on underdetermined quadratic interpolation, … Read more

Efficient composite heuristics for integer bound constrained noisy optimization

This paper discusses a composite algorithm for bound constrained noisy derivative-free optimization problems with integer variables. This algorithm is an integer variant of the matrix adaptation evolution strategy. An integer derivative-free line search strategy along affine scaling matrix directions is used to generate candidate points. Each affine scaling matrix direction is a product of the … Read more

Worst-case evaluation complexity of a derivative-free quadratic regularization method

This short paper presents a derivative-free quadratic regularization method for unconstrained minimization of a smooth function with Lipschitz continuous gradient. At each iteration, trial points are computed by minimizing a quadratic regularization of a local model of the objective function. The models are based on forward finite-difference gradient approximations. By using a suitable acceptance condition … Read more

Direct search based on probabilistic descent in reduced spaces

Derivative-free algorithms seek the minimum value of a given objective function without using any derivative information. The performance of these methods often worsen as the dimension increases, a phenomenon predicted by their worst-case complexity guarantees. Nevertheless, recent algorithmic proposals have shown that incorporating randomization into otherwise deterministic frameworks could alleviate this effect for direct-search methods. … Read more

A general mathematical framework for constrained mixed-variable blackbox optimization problems with meta and categorical variables

A mathematical framework for modelling constrained mixed-variable optimization problems is presented in a blackbox optimization context. The framework introduces a new notation and allows solution strategies. The notation framework allows meta and categorical variables to be explicitly and efficiently modelled, which facilitates the solution of such problems. The new term meta variables is used to … Read more

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

A weak tail-bound probabilistic condition for function estimation in stochastic derivative-free optimization

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