Related papers: Two-level trust-region method with random subspace…
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…
High-order (non-linear) functionals have become very popular in segmentation, stereo and other computer vision problems. Level sets is a well established general gradient descent framework, which is directly applicable to optimization of…
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…
We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational inequalities of the second kind. Under suitable assumptions on…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
A robust two-stage shape retrieval (TSR) method is proposed to address the 2D shape retrieval problem. Most state-of-the-art shape retrieval methods are based on local features matching and ranking. Their retrieval performance is not robust…
We present a reusable, open-source software implementation of the second-order trust region algorithm in the new OpenTrustRegion library. We apply the implementation to the general-purpose optimization of molecular orbitals in various…
A novel trust region method for solving linearly constrained nonlinear programs is presented. The proposed technique is amenable to a distributed implementation, as its salient ingredient is an alternating projected gradient sweep in place…
Under interpolation-type assumptions such as the strong growth condition, stochastic optimization methods can attain convergence rates comparable to full-batch methods, but their performance, particularly for SGD, remains highly sensitive…
For a multi-cell, multi-user, cellular network downlink sum-rate maximization through power allocation is a nonconvex and NP-hard optimization problem. In this paper, we present an effective approach to solving this problem through single-…
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…
A method is proposed for solving equality constrained nonlinear optimization problems involving twice continuously differentiable functions. The method employs a trust funnel approach consisting of two phases: a first phase to locate an…
Exploration systems are critical for enhancing the autonomy of robots. Due to the unpredictability of the future planning space, existing methods either adopt an inefficient greedy strategy or require a lot of resources to obtain a global…
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…
There are a large number of methods for solving under-determined linear inverse problem. Many of them have very high time complexity for large datasets. We propose a new method called Two-Stage Sparse Representation (TSSR) to tackle this…
In this paper, we study the extended trust region subproblem (eTRS) in which the trust region intersects the unit ball with a single linear inequality constraint. By reformulating the Lagrangian dual of eTRS as a two-parameter linear…
We consider the minimization of a cost function $f$ on a manifold $M$ using Riemannian gradient descent and Riemannian trust regions (RTR). We focus on satisfying necessary optimality conditions within a tolerance $\varepsilon$.…
Binary trust-region steepest descent (BTR) and combinatorial integral approximation (CIA) are two recently investigated approaches for the solution of optimization problems with distributed binary-/discrete-valued variables (control…
This study proposes a new automated strategy for designing and optimizing three-dimensional interplanetary low-thrust (LT) trajectories. The method formulates the design as a hybrid optimal control problem and solves it using a two-step…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…