Related papers: Nonmonotone Globalization for Anderson Acceleratio…

In this paper, we propose a unified two-phase scheme to accelerate any high-order regularized tensor approximation approach on the smooth part of a composite convex optimization model. The proposed scheme has the advantage of not needing to…

Existing approaches to robust global asymptotic stabilization of a pair of antipodal points on unit $n$-sphere $\mathbb{S}^n$ typically involve the non-centrally synergistic hybrid controllers for attitude tracking on unit quaternion space.…

We propose a globally convergent Gauss-Newton algorithm for finding a local optimal solution of a non-convex and possibly non-smooth optimization problem. The algorithm that we present is based on a Gauss-Newton-type iteration for the…

This study proposes a cubic regularization of the Newton method for generating weakly efficient points of unconstrained vector optimization problems under no convexity assumption on the objective function. It is observed that at a given…

We consider nonlinear inverse problems arising in the context of parameter identification for parabolic partial differential equations (PDEs). For stable reconstructions, regularization methods such as the iteratively regularized…

In this paper, we propose a globally convergent Newton type method to solve $\ell_0$ regularized sparse optimization problem. In fact, a line search strategy is applied to the Newton method to obtain global convergence. The Jacobian matrix…

We focus on minimizing nonconvex finite-sum functions that typically arise in machine learning problems. In an attempt to solve this problem, the adaptive cubic regularized Newton method has shown its strong global convergence guarantees…

This paper proposes a semidefinite relaxation for landmark-based localization with unknown data associations in planar environments. The proposed method simultaneously solves for the optimal robot states and data associations in a globally…

Acceleration of first order methods is mainly obtained via inertial techniques \`a la Nesterov, or via nonlinear extrapolation. The latter has known a recent surge of interest, with successful applications to gradient and proximal gradient…

We investigate a globalized inexact semismooth Newton method applied to strongly convex optimization problems in Hilbert spaces. Here, the semismooth Newton method is appplied to the dual problem, which has a continuously differentiable…

We provide new adaptive first-order methods for constrained convex optimization. Our main algorithms AdaACSA and AdaAGD+ are accelerated methods, which are universal in the sense that they achieve nearly-optimal convergence rates for both…

Deep neural networks have become a staple in solving intricate problems, proving their mettle in a wide array of applications. However, their training process is often hampered by shifting activation distributions during backpropagation,…

Accelerated coordinate descent is widely used in optimization due to its cheap per-iteration cost and scalability to large-scale problems. Up to a primal-dual transformation, it is also the same as accelerated stochastic gradient descent…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

This work proposes A$^2$GD, a novel adaptive accelerated gradient descent method for convex and composite optimization. Smoothness and convexity constants are updated via Lyapunov analysis. Inspired by stability analysis in ODE solvers, the…

Newton's method has been an important approach for solving variational inequalities, quasi-Newton method is a good alternative choice to save computational cost. In this paper, we propose a new method for solving monotone variational…

Non-rigid 3D registration, which deforms a source 3D shape in a non-rigid way to align with a target 3D shape, is a classical problem in computer vision. Such problems can be challenging because of imperfect data (noise, outliers and…

The ability of widely distributed radar systems to capture diverse spatial scattering properties substantially improves radar imaging performance. Traditional imaging methods leverage regularized optimization techniques to reconstruct…

We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…

A lot of theoretical and empirical evidence shows that the flatter local minima tend to improve generalization. Adversarial Weight Perturbation (AWP) is an emerging technique to efficiently and effectively find such minima. In AWP we…