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We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. Using a suitable reformulation of the given problem, our method combines the inexact…
A trust-region algorithm using inexact function and derivatives values is introduced for solving unconstrained smooth optimization problems. This algorithm uses high-order Taylor models and allows the search of strong approximate minimizers…
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 note, we present a derivative-free trust-region (TR) algorithm for reliability based optimization (RBO) problems. The proposed algorithm consists of solving a set of subproblems, in which simple surrogate models of the reliability…
The importance of Localized Molecular Orbitals in correlation treatments beyond mean-field calculation and in the illustration of chemical bonding can hardly be overstated. However, generation of orthonormal localized occupied MOs is…
We consider Riemannian inequality-constrained optimization problems. Such problems inherit the benefits of Riemannian approach developed in the unconstrained setting and naturally arise from applications in control, machine learning, and…
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…
In this paper, we propose a new and efficient nonmonotone adaptive trust region algorithm to solve unconstrained optimization problems. This algorithm incorporates two novelties: it benefits from a radius dependent shrinkage parameter for…
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…
Stochastic gradient-based optimization is crucial to optimize neural networks. While popular approaches heuristically adapt the step size and direction by rescaling gradients, a more principled approach to improve optimizers requires…
This paper addresses some trust-region methods equipped with nonmonotone strategies for solving nonlinear unconstrained optimization problems. More specifically, the importance of using nonmonotone techniques in nonlinear optimization is…
This paper presents an algorithm for the preprocessing of observation data aimed at improving the robustness of orbit determination tools. Two objectives are fulfilled: obtain a refined solution to the initial orbit determination problem…
In recent years, random subspace methods have been actively studied for large-dimensional nonconvex problems. Recent subspace methods have improved theoretical guarantees such as iteration complexity and local convergence rate while…
Bayesian Optimization (BO) is a popular framework for optimizing black-box functions. Despite its effectiveness, BO is often inefficient for high-dimensional problems due to the exponential growth of the search space, heterogeneity of the…
This work is on constrained large-scale non-convex optimization where the constraint set implies a manifold structure. Solving such problems is important in a multitude of fundamental machine learning tasks. Recent advances on Riemannian…
In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while…
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…
We introduce two multifidelity trust-region methods based on the Magical Trust Region (MTR) framework. MTR augments the classical trust-region step with a secondary, informative direction. In our approaches, the secondary ``magical''…
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…
Gray-box optimization, where parts of optimization problems are represented by algebraic models while others are treated as black-box models lacking analytic derivatives, remains a challenge. Trust-region (TR) methods provide a robust…