Related papers: Finite Termination of a Generalized Perceptron Alg…
The classical Perceptron algorithm of Rosenblatt can be used to find a linear threshold function to correctly classify $n$ linearly separable data points, assuming the classes are separated by some margin $\gamma > 0$. A foundational result…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
The Douglas-Rachford algorithm is a simple yet effective method for solving convex feasibility problems. However, if the underlying constraints are inconsistent, then the convergence theory is incomplete. We provide convergence results when…
Very recently, the papers "Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof" by Jang and Ryu, and "The Iterates of Nesterov's Accelerated Algorithm Converge in the Critical Regimes" by Bot, Fadili, and…
Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters…
The structure of the F5 algorithm to compute Gr\"obner bases makes it very efficient. However, while it is believed to terminate for so-called regular sequences, it is not clear whether it terminates for all inputs. This paper has two major…
We prove the convergence of the proximal point algorithm for finding the unique minimizer of a strongly quasiconvex function in general nonlinear Hadamard spaces, generalizing a recent result due to F. Lara. Our argument is rather…
We analyze the convergence rate of the monotone accelerated proximal gradient method, which can be used to solve structured convex composite optimization problems. A linear convergence rate is established when the smooth part of the…
Given a frame in a finite dimensional Hilbert space we construct additive perturbations which decrease the condition number of the frame. By iterating this perturbation, we introduce an algorithm that produces a tight frame in a finite…
In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining its correctness by fully characterizing the problems that are…
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…
In many problems in machine learning and operations research, we need to optimize a function whose input is a random variable or a probability density function, i.e. to solve optimization problems in an infinite dimensional space. On the…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We analyze various Lipschitz…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
In this paper we present a unifying framework for continuous optimization methods grounded in the concept of generalized convexity. Utilizing the powerful theory of $\Phi$-convexity, we propose a conceptual algorithm that extends the…
We study the convergence of the gradient descent method for solving ill-posed problems where the solution is characterized as a global minimum of a differentiable functional in a Hilbert space. The classical least-squares functional for…