Related papers: An Optimal Interpolation Set for Model-Based Deriv…
We present a novel derivative-free interpolation based optimization algorithm. A trust-region method is used where a surrogate model is realized via an interpolation framework. The framework for interpolation is provided by Universal…
Derivative-free optimization problems are optimization problems where derivative information is unavailable. The least Frobenius norm updating quadratic interpolation model function is one of the essential under-determined model functions…
We consider interpolation-based derivative-free optimization in settings where only some derivatives are available. Such situations arise naturally in scientific computing applications involving simulations, adjoint-enabled components,…
Derivative-free optimization methods are numerical methods for optimization problems in which no derivative information is used. Such optimization problems are widely seen in many real applications. One particular class of derivative-free…
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…
Adaptive sampling with interpolation-based trust regions or ASTRO-DF is a successful algorithm for stochastic derivative-free optimization with an easy-to-understand-and-implement concept that guarantees almost sure convergence to a…
In many applications of mathematical optimization, one may wish to optimize an objective function without access to its derivatives. These situations call for derivative-free optimization (DFO) methods. Among the most successful approaches…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
In this paper (part 1), we describe a derivative-free trust-region method for solving unconstrained optimization problems. We will discuss a method when we relax the model order assumption and use artificial neural network techniques to…
This paper introduces a new framework for constructing the Discrete Empirical Interpolation Method DEIM projection operator. The interpolation node selection procedure is formulated using the QR factorization with column pivoting, and it…
We develop a new approximation theory for linear and quadratic interpolation models, suitable for use in convex-constrained derivative-free optimization (DFO). Most existing model-based DFO methods for constrained problems assume the…
Complexity analysis has become an important tool in the convergence analysis of optimization algorithms. For derivative-free optimization algorithms, it is not different. Interestingly, several constants that appear when developing…
Non-monotone trust-region methods are known to provide additional benefits for scalar and multi-objective optimization, such as enhancing the probability of convergence and improving the speed of convergence. For optimization of set-valued…
We propose UPOQA, a derivative-free optimization algorithm for partially separable unconstrained problems, leveraging quadratic interpolation and a structured trust-region framework. By decomposing the objective into element functions,…
The field of derivative-free optimization (DFO) studies algorithms for nonlinear optimization that do not rely on the availability of gradient or Hessian information. It is primarily designed for settings when functions are black-box,…
In this work, we present a trust-region optimization framework that employs Hermite kernel surrogate models. The method targets optimization problems with computationally demanding objective functions, for which direct optimization is often…
In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…
In this article, we develop a trust-region technique to find critical points of unconstrained set optimization problems with the objective set-valued map defined by finitely many twice continuously differentiable functions. The technique is…
In this paper we consider the use of probabilistic or random models within a classical trust-region framework for optimization of deterministic smooth general nonlinear functions. Our method and setting differs from many stochastic…
Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal…