Related papers: A Multi-Precision Quadratic Regularization Method …
In this paper we consider the cubic regularization (CR) method for minimizing a twice continuously differentiable function. While the CR method is widely recognized as a globally convergent variant of Newton's method with superior iteration…
The $\chi^2$-principle generalizes the Morozov discrepancy principle (MDP) to the augmented residual of the Tikhonov regularized least squares problem. Weighting of the data fidelity by a known Gaussian noise distribution on the measured…
Sparse learning has recently received increasing attention in many areas including machine learning, statistics, and applied mathematics. The mixed-norm regularization based on the l1q norm with q>1 is attractive in many applications of…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
Recently, Greg\'orio and Oliveira developed a proximal point scalarization method (applied to multi-objective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of…
Data augmentation has been proven to be an effective technique for developing machine learning models that are robust to known classes of distributional shifts (e.g., rotations of images), and alignment regularization is a technique often…
Multiplicative errors in addition to spatially referenced observations often arise in geodetic applications, particularly in surface estimation with light detection and ranging (LiDAR) measurements. However, spatial regression involving…
Accurate extrinsic calibration between LiDAR and camera sensors is important for reliable perception in autonomous systems. In this paper, we present a novel multi-objective optimization framework that jointly minimizes the geometric…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer…
We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. Our approach first solves a L1 penalized version of the NP-hard sparse PCA optimization problem and then uses a randomized…
A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function…
Gaussian Process Regression (GPR) is an important type of supervised machine learning model with inherent uncertainty measure in its predictions. We propose a new framework, nuGPR, to address the well-known challenge of high computation…
We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…
Cubic regularization (CR) is an optimization method with emerging popularity due to its capability to escape saddle points and converge to second-order stationary solutions for nonconvex optimization. However, CR encounters a high sample…
This paper presents a multi-objective stochastic optimization method for tuning of the controller parameters of Refrigeration Systems based on Vapour Compression. Stochastic Multi Parameter Divergence Optimization (SMDO) algorithm is…
In recommender systems, a common problem is the presence of various biases in the collected data, which deteriorates the generalization ability of the recommendation models and leads to inaccurate predictions. Doubly robust (DR) learning…
Explicit stabilized methods are highly efficient time integrators for large and stiff systems of ordinary differential equations especially when applied to semi-discrete parabolic problems. However, when local spatial mesh refinement is…