scholarly journals On a New Optimization Method With Constraints

2020 ◽  
Vol 12 (5) ◽  
pp. 27
Author(s):  
Bouchta x RHANIZAR
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Convex Set ◽  
Optimization Method ◽  
New Method ◽  
Constrained Optimization Problem ◽  
Numerical Examples ◽  
Unconstrained Problem ◽  
Closed Convex Set

We consider the constrained optimization problem  defined by: $$f(x^*) = \min_{x \in  X} f(x) \eqno (1)$$ where the function  $f$ : $ \pmb{\mathbb{R}}^{n} \longrightarrow \pmb{\mathbb{R}}$ is convex  on a closed convex set X. In this work, we will give a new method to solve problem (1) without bringing it back to an unconstrained problem. We study the convergence of this new method and give numerical examples.

Lateral Dynamics Optimization of a Conventional Railcar

1975 ◽  
Vol 97 (3) ◽  
pp. 293-299 ◽  
Author(s):  
N. K. Cooperrider ◽  
J. J. Cox ◽  
J. K. Hedrick
Keyword(s):  
Constrained Optimization ◽  
High Speed ◽  
Optimization Problem ◽  
Ride Comfort ◽  
Stability Margin ◽  
Railway Vehicle ◽  
Constrained Optimization Problem ◽  
Stroke Length ◽  
Car Body ◽  
Unconstrained Problem

The attempt to develop a railway vehicle that can operate in the 150 to 300-mph(240 to 480-km/h) speed regime is seriously hampered by the problems of ride comfort, curve negotiation, and “hunting.” This latter phenomena involves sustained lateral oscillations that occur above certain critical forward velocities and cause large dynamic loads between the wheels and track as well as contributing to passenger discomfort. This paper presents results of an initial effort to solve these problems by utilizing optimization procedures to design a high speed railway vehicle. This study indicates that the problem is more easily treated as a constrained optimization problem than as an unconstrained problem with several terms in the objective function. In the constrained optimization problem, the critical “hunting” speed was maximized subject to constraints on 1) the acceleration of the car body, 2) the suspension stroke length, and 3) the maximum suspension stroke while negotiating a curve. A simple, three degree-of-freedom model of the rail vehicle was used for this study. Solutions of this constrained problem show that beyond a minimum yaw stiffness between truck and car body the operating speed remains nearly constant. Thus, above this value, the designer may trade off yaw stiffness, wheel tread conicity and stability margin.

scholarly journals Superlinear Convergence of a Modified Newton's Method for Convex Optimization Problems With Constraints

2021 ◽  
Vol 13 (2) ◽  
pp. 90
Author(s):  
Bouchta RHANIZAR
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Convex Set ◽  
Optimization Problems ◽  
Descent Direction ◽  
Constrained Optimization Problem ◽  
Constrained Optimization Problems ◽  
Convex Optimization Problems ◽  
Definition Of ◽  
Bounded Convex

We consider the constrained optimization problem  defined by: $$f (x^*) = \min_{x \in  X} f(x)\eqno (1)$$ where the function  f : \pmb{\mathbb{R}}^{n} → \pmb{\mathbb{R}} is convex  on a closed bounded convex set X. To solve problem (1), most methods transform this problem into a problem without constraints, either by introducing Lagrange multipliers or a projection method. The purpose of this paper is to give a new method to solve some constrained optimization problems, based on the definition of a descent direction and a step while remaining in the X convex domain. A convergence theorem is proven. The paper ends with some numerical examples.

scholarly journals Nonconvex constrained optimization by a filtering branch and bound

2020 ◽  
Author(s):  
Gabriele Eichfelder ◽  
Kathrin Klamroth ◽  
Julia Niebling
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Constrained Optimization Problem ◽  
Numerical Tests ◽  
Nonconvex Constrained Optimization ◽  
Objective Value ◽  
Feasible Solutions ◽  
Quality Guarantee ◽  
Single Objective

AbstractA major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the $$\alpha $$ α BB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained optimization problem. Moreover, the multiobjective reformulation enables to identify the trade-off between constraint satisfaction and objective value which is also reflected in the quality guarantee. Numerical tests validate that we indeed can find feasible and often optimal solutions where the classical single-objective $$\alpha $$ α BB method fails, i.e., it terminates without ever finding a feasible solution.

scholarly journals Optimal P-Q Control of Grid-Connected Inverters in a Microgrid Based on Adaptive Population Extremal Optimization

Energies ◽  
2018 ◽  
Vol 11 (8) ◽  
pp. 2107 ◽  
Author(s):  
Min-Rong Chen ◽  
Huan Wang ◽  
Guo-Qiang Zeng ◽  
Yu-Xing Dai ◽  
Da-Qiang Bi
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Reactive Power ◽  
Active Power ◽  
Adaptive Genetic Algorithm ◽  
Constrained Optimization Problem ◽  
Extremal Optimization ◽  
Active And Reactive Power ◽  
Three Phase ◽  
Grid Connected Inverter

The optimal P-Q control issue of the active and reactive power for a microgrid in the grid-connected mode has attracted increasing interests recently. In this paper, an optimal active and reactive power control is developed for a three-phase grid-connected inverter in a microgrid by using an adaptive population-based extremal optimization algorithm (APEO). Firstly, the optimal P-Q control issue of grid-connected inverters in a microgrid is formulated as a constrained optimization problem, where six parameters of three decoupled PI controllers are real-coded as the decision variables, and the integral time absolute error (ITAE) between the output and referenced active power and the ITAE between the output and referenced reactive power are weighted as the objective function. Then, an effective and efficient APEO algorithm with an adaptive mutation operation is proposed for solving this constrained optimization problem. The simulation and experiments for a 3kW three-phase grid-connected inverter under both nominal and variable reference active power values have shown that the proposed APEO-based P-Q control method outperforms the traditional Z-N empirical method, the adaptive genetic algorithm-based, and particle swarm optimization-based P-Q control methods.

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