Optimal convergence rate

In this paper, we study the convergence and convergence rates of damped Newton algorithms for solving unconstrained optimization problems with twice continuously differentiable objective functions.

14p visergeyne 18-06-2024 2 0   Download

In this paper, we propose a generalized Nesterov algorithm for the constrained optimization problems on a closed convex set. We prove the convergence as well as the convergence rate of the proposed algorithm. First, we present a new algorithm based on the generalization of Nesterov’s algorithm.

5p vigojek 02-02-2024 1 0   Download

In this section, we recall some notations and properties of differentiable convex functions, differentiable functions that the gradient vectors are Lipschitz contiuous. These notations and properties are used in the proofs of main results in this paper.

4p vipatriciawoertz 30-05-2022 8 1   Download

Nonconvex SINR constraints in amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay beamforming problems make the design mathematically intractable. A more practical optimization is to maximize the minimum SINR achievable data rate among all the users. The previously existing methods invoke the vectorization of pre-coding matrix X and then introduce the auxiliary variable matrix of lager dimension which results in an increased computational complexity.

5p viericschmid 12-01-2022 14 2   Download

The purpose of this paper is to present a new and an alternative differential evolution (ADE) algorithm for solving unconstrained global optimization problems. In the new algorithm, a new directed mutation rule is introduced based on the weighted difference vector between the best and the worst individuals of a particular generation. The mutation rule is combined with the basic mutation strategy through a linear decreasing probability rule. This modification is shown to enhance the local search ability of the basic DE and to increase the convergence rate.

17p kethamoi1 17-11-2019 20 1   Download

This paper proposes a Hybrid Improved Bacterial Swarm (HIBS) optimization algorithm for the minimization of Equal Error Rate (EER) as a performance measure in a hand-based multimodal biometric authentication system. The hybridization of the algorithm was conducted by incorporating Bacterial Foraging Optimization (BFO) and Particle Swarm Optimization (PSO) algorithm to mitigate weaknesses in slow and premature convergence.

19p meriday 20-04-2019 30 2   Download

In this paper an algorithm for minimization of a nondifferentiable function is presented. The algorithm uses the Moreau-Yosida regularization of the objective function and its second order Dini upper directional derivative. The purpose of the paper is to establish general hypotheses for this algorithm, under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of the convergence.

13p vinguyentuongdanh 19-12-2018 26 0   Download

In this paper an algorithm for LC1 unconstrained optimization problems, which uses the second order Dini upper directional derivative is considered. The purpose of the paper is to establish general algorithm hypotheses under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of convergence.

6p vinguyentuongdanh 20-12-2018 25 1   Download

The Basel Committee on Banking Supervision, after an extensive consultation process, redrafted its recommendations for credit institutions’ regulatory capital requirements (Basel I) issued in 1988. The revision was motivated by the wish to adequately refl ect current developments in banking and to strengthen the stability of the international fi nancial system.

42p taisaovanchuavo 23-01-2013 52 6   Download