On the Accelerated Convergence of the Decentralized Event-triggered Algorithm for Convex Optimization

2021 ◽  
Vol 30 (01) ◽  
pp. 2140003
Author(s):  
Keke Zhang ◽  
Jiang Xiong ◽  
Xiangguang Dai
Keyword(s):  
Cost Function ◽  
Optimal Solution ◽  
Linear Convergence ◽  
Step Size ◽  
Undirected Network ◽  
Momentum Coefficient ◽  
Convex Cost ◽  
Local Convex ◽  
The Cost ◽  
Event Triggered

This article considers a problem of solving the optimal solution of the sum of locally convex cost functions over an undirected network. Each local convex cost function in the network is accessed only by each unit. To be able to reduce the amount of computation and get the desired result in an accelerated way, we put forward a fresh accelerated decentralized event-triggered algorithm, named as A-DETA, for the optimization problem. A-DETA combines gradient tracking and two momentum accelerated terms, adopts nonuniform step-sizes and emphasizes that each unit interacts with neighboring units independently only at the sampling time triggered by the event. On the premise of assuming the smoothness and strong convexity of the cost function, it is proved that A-DETA can obtain the exact optimal solution linearly in the event of sufficiently small positive step-size and momentum coefficient. Moreover, an explicit linear convergence speed is definitely shown. Finally, extensive simulation example validates the usability of A-DETA.

scholarly journals Selection model of work technology based on multi–criteria evaluations

2020 ◽  
Vol 164 ◽  
pp. 08030
Author(s):  
Sergey Barkalov ◽  
Pavel Kurochka ◽  
Anton Khodunov ◽  
Natalia Kalinina
Keyword(s):  
Cost Function ◽  
Optimal Solution ◽  
Budget Constraint ◽  
Pareto Optimal Solution ◽  
Pareto Optimal ◽  
Customer Preferences ◽  
Optimal Solution Set ◽  
The Cost ◽  
Comprehensive Indicator ◽  
Selection Of

A model for the selection of options for the production of work in a construction project is considered, when each option is characterized by a set of criteria. The number of analyzed options is being reduced based on the construction of the Pareto-optimal solution set. The remaining options are used to solve the problem based on the network model,\ in which the solution will be a subcritical path that meets budgetary constraints. At the same time, the proposed comprehensive indicator characterizing the preferences of the customer makes it possible to determine alternative options for performing work in the energy project in such a way that the amount of costs allocated to implement the set of work under consideration is minimal. Another statement of the problem is also considered when it is necessary to determine a strategy for the implementation of an energy project that, given a planned budget constraint, maximizes the growth of a comprehensive indicator that characterizes customer preferences in this project. The solution of the tasks is given under the assumption of the convexity of the cost function.

A cost minimisation model for system reliability allocation

2019 ◽  
Vol 36 (9) ◽  
pp. 1620-1643 ◽  
Author(s):  
Omkarprasad S. Vaidya ◽  
L. Ganapathy ◽  
Sushil Kumar
Keyword(s):  
Optimization Problem ◽  
Cost Optimization ◽  
Optimal Solution ◽  
System Component ◽  
Lagrangian Multiplier ◽  
Step Size ◽  
Exponential Relationship ◽  
Content Type ◽  
In Series ◽  
The Cost

Purpose The purpose of this paper is to consider a nonlinear problem of minimizing the cost of providing reliable systems. The authors assume that the system consists of several components in series, and for each such component, the cost of the component increases exponentially with its reliability. Design/methodology/approach In order to solve this nonlinear optimization problem, the authors propose two approaches. The first approach is based on the concept of adjusting the reliability of a pair of components to minimize the cost of the system. The authors call this procedure as reliability adjustment routine (RAR). Proofs of optimality and convergence for the proposed model are also provided. The second approach solves the problem by using a Lagrangian multiplier. A procedure is developed to obtain the maximum step size to achieve the desired optimal solution in minimum iterations. Proposed approaches are efficient and give exact solutions. Findings Proposed methods enable a decision maker to allocate reliability to the components in series while minimizing the total cost of the system. The developed procedures are illustrated using a numerical example. Although an exponential relationship between the component cost and reliability is assumed, this can be extended to various other nonlinear distributions. Originality/value This cost optimization problem, subject to system component reliability values, assumes the near practical nonlinear pattern of cost vs reliability. Such problems are complex to solve. The authors provide a unique approach called RAR to solve such convoluted problems. The authors also provide an approach to solve such problems by using a Lagrangian multiplier method. Various proofs have been worked out to substantiate the work.

scholarly journals MIN-MAX SOLUTIONS FOR PARAMETRIC CONTINUOUS STATIC GAME UNDER ROUGHNESS (PARAMETERS IN THE COST FUNCTION AND FEASIBLE REGION IS A ROUGH SET)

2020 ◽  
Vol 6 (2) ◽  
pp. 3
Author(s):  
Yousria A. Aboelnaga ◽  
Mai Zidan
Keyword(s):  
Cost Function ◽  
Parametric Study ◽  
Optimal Solution ◽  
Feasible Region ◽  
Roughness Parameters ◽  
Static Game ◽  
Solution Approach ◽  
Solution Point ◽  
The Stability ◽  
The Cost

Any simple perturbation in a part of the game whether in the cost function and/or conditions is a big problem because it will require a game re-solution to obtain the perturbed optimal solution. This is a waste of time because there are methods required several steps to obtain the optimal solution, then at the end we may find that there is no solution. Therefore, it was necessary to find a method to ensure that the game optimal solution exists in the case of a change in the game data. This is the aim of this paper. We first provided a continuous static game rough treatment with Min-Max solutions, then a parametric study for the processing game and called a parametric rough continuous static game (PRCSG). In a Parametric study, a solution approach is provided based on the parameter existence in the cost function that reflects the perturbation that may occur to it to determine the parameter range in which the optimal solution point keeps in the surely region that is called the stability set of the \(1^{st}\) kind. Also the sets of possible upper and lower stability to which the optimal solution belongs are characterized. Finally, numerical examples are given to clarify the solution algorithm.

scholarly journals Modified Variable Step Size FLOM-CMA Based on Lorentzian Function under Impulse Noise

2018 ◽  
Vol 232 ◽  
pp. 04061
Author(s):  
Xichang Liao ◽  
Yingke Lei
Keyword(s):  
Cost Function ◽  
Impulse Noise ◽  
Variable Step Size ◽  
Step Size ◽  
Simulation Experiments ◽  
Phase Rotation ◽  
Lorentzian Function ◽  
Equalization Algorithm ◽  
Variable Step ◽  
The Cost

Aiming at the problem that the traditional equalization algorithm under impulse noise is difficult to suppress impulse noise and achieve equalization, a new modified variable step size FLOM-CMA algorithm based on Lorentzian function is proposed in this paper. The proposed algorithm has modified the cost function to made full use of the phase information of signal to correct the phase rotation. Also, by adjusting the FLOM of cost function, that impulse noise is restrained effectively. Furthermore, the Lorentzian function is use to update the step size to make sure it is is appropriate for each equalization point. Simulation experiments show that, compared with FLOM-CMA and VS-FLOM-CMA, the proposed algorithm that the proposed algorithm achieves higher convergence accuracy with similar convergence speed. And under different impulse noise conditions, the robustness of the algorithm is better.

scholarly journals ADMM-EM Method forL1-Norm Regularized Weighted Least Squares PET Reconstruction

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Yueyang Teng ◽  
Hang Sun ◽  
Chen Guo ◽  
Yan Kang
Keyword(s):  
Cost Function ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Step Size ◽  
Lagrangian Multipliers ◽  
Positron Emission ◽  
Em Method ◽  
Image Pixels ◽  
Pet Reconstruction ◽  
The Cost

TheL1-norm regularization is usually used in positron emission tomography (PET) reconstruction to suppress noise artifacts while preserving edges. The alternating direction method of multipliers (ADMM) is proven to be effective for solving this problem. It sequentially updates the additional variables, image pixels, and Lagrangian multipliers. Difficulties lie in obtaining a nonnegative update of the image. And classic ADMM requires updating the image by greedy iteration to minimize the cost function, which is computationally expensive. In this paper, we consider a specific application of ADMM to theL1-norm regularized weighted least squares PET reconstruction problem. Main contribution is derivation of a new approach to iteratively and monotonically update the image while self-constraining in the nonnegativity region and the absence of a predetermined step size. We give a rigorous convergence proof on the quadratic subproblem of the ADMM algorithm considered in the paper. A simplified version is also developed by replacing the minima of the image-related cost function by one iteration that only decreases it. The experimental results show that the proposed algorithm with greedy iterations provides a faster convergence than other commonly used methods. Furthermore, the simplified version gives a comparable reconstructed result with far lower computational costs.

HEURISTIC OPTIMIZATION OF THE FOUNDATION OF A DYNAMICALLY STRESSED ROTATING MACHINE USING THE LATE ACCEPTANCE HILL CLIMBING (LAHC) ALGORITHM

10.6036/9762 ◽  
2021 ◽  
Vol 96 (5) ◽  
pp. 498-504
Author(s):  
JUAN LUIS TERRADEZ MARCO ◽  
ANTONIO HOSPITALER PEREZ ◽  
VICENTE ALBERO GABARDA
Keyword(s):  
Cost Function ◽  
Random Search ◽  
Optimal Solution ◽  
Hill Climbing ◽  
Dynamic Loads ◽  
Rotating Machine ◽  
Permanent Working ◽  
The Cost ◽  
Late Acceptance Hill Climbing

This paper proposal the optimization of a foundation for rotative machine under dynamic loads in transient and permanent working mode. The foundation depends on fix parameters and 37 variables. Functional constraints are defined for the foundation. A cost function depending on the variables is defined to be minimized to find the optimal. From all the possible solutions, only are selected the ones that validate the constrains and minimize the cost function. The search of the optimal solution is made with an algorithm of random search by “neighbouring of one point” called Last Acceptance Hill Climbing(LAHC). It is an algorithm of the type called “Adaptative Memory Programming” (AMP) that accepts worse solutions to get the local minimum and learns of the results of the search. The algorithm only depends on the length of the comparison vector and the stop criteria. 350 experiences were made with different length of the comparison vector. It was analysed the quality of the optimal solutions got it with each length of the vector. Quality of the set of solutions was compared fitting them to a 3 parameters Weibull distribution.

OPTIMAL FEASIBLE SOLUTIONS TO A ROAD FREIGHT TRANSPORTATION PROBLEM

2020 ◽  
Vol 5 (1) ◽  
pp. 456
Author(s):  
Tolulope Latunde ◽  
Joseph Oluwaseun Richard ◽  
Opeyemi Odunayo Esan ◽  
Damilola Deborah Dare
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Transportation Cost ◽  
North West ◽  
Life Problems ◽  
Basic Feasible Solutions ◽  
Feasible Solutions ◽  
Road Freight Transportation ◽  
The Cost ◽  
Cost Of Transportation

For twenty decades, there is a visible ever forward advancement in the technology of mobility, vehicles and transportation system in general. However, there is no "cure-all" remedy ideal enough to solve all life problems but mathematics has proven that if the problem can be determined, it is most likely solvable. New methods and applications will keep coming to making sure that life problems will be solved faster and easier. This study is to adopt a mathematical transportation problem in the Coca-Cola company aiming to help the logistics department manager of the Asejire and Ikeja plant to decide on how to distribute demand by the customers and at the same time, minimize the cost of transportation. Here, different algorithms are used and compared to generate an optimal solution, namely; North West Corner Method (NWC), Least Cost Method (LCM) and Vogel’s Approximation Method (VAM). The transportation model type in this work is the Linear Programming as the problems are represented in tables and results are compared with the result obtained on Maple 18 software. The study shows various ways in which the initial basic feasible solutions to the problem can be obtained where the best method that saves the highest percentage of transportation cost with for this problem is the NWC. The NWC produces the optimal transportation cost which is 517,040 units.

scholarly journals Convergence rate analysis of an iterative algorithm for solving the multiple-sets split equality problem

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shijie Sun ◽  
Meiling Feng ◽  
Luoyi Shi
Keyword(s):  
Convergence Rate ◽  
Iterative Algorithm ◽  
Sufficient Conditions ◽  
Linear Convergence ◽  
Regularity Property ◽  
Step Size ◽  
Bounded Linear ◽  
Split Equality Problem ◽  
Linear Convergence Rate ◽  
Equality Problem

Abstract This paper considers an iterative algorithm of solving the multiple-sets split equality problem (MSSEP) whose step size is independent of the norm of the related operators, and investigates its sublinear and linear convergence rate. In particular, we present a notion of bounded Hölder regularity property for the MSSEP, which is a generalization of the well-known concept of bounded linear regularity property, and give several sufficient conditions to ensure it. Then we use this property to conclude the sublinear and linear convergence rate of the algorithm. In the end, some numerical experiments are provided to verify the validity of our consequences.

scholarly journals Inclusion of Hydraulic Controls in Rehabilitation Models of Drainage Networks to Control Floods

Water ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 514
Author(s):  
Leonardo Bayas-Jiménez ◽  
F. Javier Martínez-Solano ◽  
Pedro L. Iglesias-Rey ◽  
Daniel Mora-Melia ◽  
Vicente S. Fuertes-Miquel
Keyword(s):  
Genetic Algorithm ◽  
Drainage System ◽  
Optimal Solution ◽  
Hydraulic Control ◽  
Drainage Systems ◽  
Storm Water Management Model ◽  
Drainage Networks ◽  
Extreme Rain ◽  
Rain Events ◽  
The Cost

A problem for drainage systems managers is the increase in extreme rain events that are increasing in various parts of the world. Their occurrence produces hydraulic overload in the drainage system and consequently floods. Adapting the existing infrastructure to be able to receive extreme rains without generating consequences for cities’ inhabitants has become a necessity. This research shows a new way to improve drainage systems with minimal investment costs, using for this purpose a novel methodology that considers the inclusion of hydraulic control elements in the network, the installation of storm tanks and the replacement of pipes. The presented methodology uses the Storm Water Management Model for the hydraulic analysis of the network and a modified Genetic Algorithm to optimize the network. In this algorithm, called the Pseudo-Genetic Algorithm, the coding of the chromosomes is integral and has been used in previous studies of hydraulic optimization. This work evaluates the cost of the required infrastructure and the damage caused by floods to find the optimal solution. The main conclusion of this study is that the inclusion of hydraulic controls can reduce the cost of network rehabilitation and decrease flood levels.

scholarly journals An Adaptive Optimization Method Based on Learning Rate Schedule for Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 850
Author(s):  
Dokkyun Yi ◽  
Sangmin Ji ◽  
Jieun Park
Keyword(s):  
Artificial Intelligence ◽  
Cost Function ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Optimization Method ◽  
Learning Method ◽  
Adaptive Optimization ◽  
The Cost ◽  
Proof Of Convergence ◽  
Learning Data

Artificial intelligence (AI) is achieved by optimizing the cost function constructed from learning data. Changing the parameters in the cost function is an AI learning process (or AI learning for convenience). If AI learning is well performed, then the value of the cost function is the global minimum. In order to obtain the well-learned AI learning, the parameter should be no change in the value of the cost function at the global minimum. One useful optimization method is the momentum method; however, the momentum method has difficulty stopping the parameter when the value of the cost function satisfies the global minimum (non-stop problem). The proposed method is based on the momentum method. In order to solve the non-stop problem of the momentum method, we use the value of the cost function to our method. Therefore, as the learning method processes, the mechanism in our method reduces the amount of change in the parameter by the effect of the value of the cost function. We verified the method through proof of convergence and numerical experiments with existing methods to ensure that the learning works well.

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