Related papers: Random projections for trust region subproblems
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 paper, a globally convergent trust region proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
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…
We propose a trust-region type method for a class of nonsmooth nonconvex optimization problems where the objective function is a summation of a (probably nonconvex) smooth function and a (probably nonsmooth) convex function. The model…
We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include…
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…
Model-based derivative-free optimization (DFO) methods are an important class of DFO methods that are known to struggle with solving high-dimensional optimization problems. Recent research has shown that incorporating random subspaces into…
An algorithm is proposed for solving stochastic and finite sum minimization problems. Based on a trust region methodology, the algorithm employs normalized steps, at least as long as the norms of the stochastic gradient estimates are within…
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…
Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple…
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…
A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…
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…
In this paper, we study a few challenging theoretical and numerical issues on the well known trust region policy optimization for deep reinforcement learning. The goal is to find a policy that maximizes the total expected reward when the…
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…
We present a flexible trust region descend algorithm for unconstrained and convexly constrained multiobjective optimization problems. It is targeted at heterogeneous and expensive problems, i.e., problems that have at least one objective…
The trust region subproblem (TRS) is to minimize a possibly nonconvex quadratic function over a Euclidean ball. There are typically two cases for (TRS), the so-called ``easy case'' and ``hard case''. Even in the ``easy case'', the sequence…
There is a recent proliferation of research on the integration of machine learning and optimization. One expansive area within this research stream is predictive-model embedded optimization, which proposes the use of pre-trained predictive…
Stochastic minimax optimization has drawn much attention over the past decade due to its broad applications in machine learning, signal processing and game theory. In some applications, the probability distribution of uncertainty depends on…
We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models. Especially, we propose a specific algorithm, termed STRME, in which the trust-region radius depends linearly on the…