相关论文: A non-smooth trust-region method for locally Lipsc…
In this work, we present a heretofore unseen application of Ising machines to perform trust region-based optimisation with box constraints. This is done by considering a specific form of opto-electronic oscillator-based coherent Ising…
Lipschitz continuity of the gradient mapping of a continuously differentiable function plays a crucial role in designing various optimization algorithms. However, many functions arising in practical applications such as low rank matrix…
We use a non-smooth trust-region method for $H_\infty$-control of infinite-dimensional systems. Our method applies in particular to distributed and boundary control of partial differential equations. It is computationally attractive as it…
The trust region method is an algorithm traditionally used in the field of derivative free optimization. The method works by iteratively constructing surrogate models (often linear or quadratic functions) to approximate the true objective…
In this paper, a new alternating direction trust region method based on conic model is used to solve unconstrained optimization problems. By use of the alternating direction method, the new conic model trust region subproblem is solved by…
We introduce a two-level trust-region method (TLTR) for solving unconstrained nonlinear optimization problems. Our method uses a composite iteration step, which is based on two distinct search directions. The first search direction is…
We present a new approach to the problem of stationary viscoplastic duct flow as modelled by the Herschel-Bulkley model, with Bingham fluids included as a special case. While the mathematical formulation of this problem is conventionally…
We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For…
This technical note considers a distributed convex optimization problem with nonsmooth cost functions and coupled nonlinear inequality constraints. To solve the problem, we first propose a modified Lagrangian function containing local…
The Trust Region Subproblem is a fundamental optimization problem that takes a pivotal role in Trust Region Methods. However, the problem, and variants of it, also arise in quite a few other applications. In this article, we present a…
We present the Trust Region Adversarial Functional Subdifferential (TRAFS) algorithm for constrained optimization of nonsmooth convex Lipschitz functions. Unlike previous methods that assume a subgradient oracle model, we work with the…
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…
Convex and nonconvex finite-sum minimization arises in many scientific computing and machine learning applications. Recently, first-order and second-order methods where objective functions, gradients and Hessians are approximated by…
In this paper, we revisit the classical problem of solving over-determined systems of nonsmooth equations numerically. We suggest a nonsmooth Levenberg--Marquardt method for its solution which, in contrast to the existing literature, does…
Stochastic non-smooth convex optimization constitutes a class of problems in machine learning and operations research. This paper considers minimization of a non-smooth function based on stochastic subgradients. When the function has a…
Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulation of the bilevel problem, but its utility is often limited…
This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivative-free methods are proposed and developed for minimizing…
Motivated by TRACE algorithm [Curtis et al. 2017], we propose a trust region algorithm for finding second order stationary points of a linearly constrained non-convex optimization problem. We show the convergence of the proposed algorithm…
We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and…
This paper considers the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on the algebraic variety of real matrices of upper-bounded rank. This problem is known to enable the formulation of various…