Related papers: On convergence to the global optima

We propose some algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. With the key observation of the velocity observable and controllable in the…

We prove that it is impossible to built a universal quantum machine that produces reflections about an unknown state. We then point out a connection between this result and the optimality of Grover's search algorithm: if such reflection…

We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…

We prove that there is no algorithm to decide whether a given integer vector is in the closure of the entropic cone $\overline{\Gamma_{n}^{*}}$. Equivalently, there is no decision procedure to determine whether a given integer-valued…

In this paper, we analyze some theoretical properties of the problem of minimizing a quadratic function with a cubic regularization term, arising in many methods for unconstrained and constrained optimization that have been proposed in the…

Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…

The adaptive optimizer for training neural networks has continually evolved to overcome the limitations of the previously proposed adaptive methods. Recent studies have found the rare counterexamples that Adam cannot converge to the optimal…

Global minimization is a fundamental challenge in optimization, especially in machine learning, where finding the global minimum of a function directly impacts model performance and convergence. This article introduces a novel optimization…

This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…

We analyze a zeroth-order particle algorithm for the global optimization of a non-convex function, focusing on a variant of Consensus-Based Optimization (CBO) with small but fixed noise intensity. Unlike most previous studies restricted to…

We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected,…

In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal…

In a real Hilbert space $\mathcal{H}$. Given any function $f$ convex differentiable whose solution set $\argmin_{\mathcal{H}}\,f$ is nonempty, by considering the Proximal Algorithm $x_{k+1}=\text{prox}_{\b_k f}(d x_k)$, where $0<d<1$ and…

Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…

In this article, we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis. Monotonic convergence for a general class of multiplicative algorithms for $D$-optimality has been…

We study unconstrained control of a two-level quantum system and analyse critical points of the objective functional which represents quantum average of system observable at some final time $T$. In Proc. Steklov Inst. Math. 285, 233-240…

Locating proximal points is a component of numerous minimization algorithms. This work focuses on developing a method to find the proximal point of a convex function at a point, given an inexact oracle. Our method assumes that exact…

In the past several years, there have been several representative attitude determination methods developed using derivative-based optimization algorithms. Optimization techniques e.g. gradient-descent algorithm (GDA), Gauss-Newton algorithm…

We consider minimizing a sum of non-smooth objective functions with set constraints in a distributed manner. As to this problem, we propose a distributed algorithm with an exponential convergence rate for the first time. By the exact…

First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…