scholarly journals A necessary condition for a mayer type set-valued optimization problem governed by a discrete inclusion system

2021 ◽  
Author(s):  
Özkan Deǧer
Keyword(s):  
Optimization Problem ◽  
Necessary Condition ◽  
Discrete Inclusion

scholarly journals On an extremum problem

1987 ◽  
Vol 28 (3) ◽  
pp. 376-392 ◽  
Author(s):  
Joanna Matula
Keyword(s):  
Existence Theorem ◽  
Optimization Problem ◽  
Integral Functional ◽  
Integral Form ◽  
Extremum Problem ◽  
Necessary Condition

AbstractWe consider an optimization problem in which the function being minimized is the sum of the integral functional and the full variation of control. For this problem, we prove the existence theorem, a necessary condition in an integral form and a local necessary condition in the case of monotonic controls.

scholarly journals INFORMATION TECHNOLOGY OF TERRITORY COVERING BY SENSORS WITH THE CONSTANT INTERSECTION LEVEL AND COST MINIMIZATION

2020 ◽  
pp. 65-72
Author(s):  
V.Y. Petrivskyi ◽  
V.L. Shevchenko ◽  
O.S. Bychkov ◽  
V.M. Loza
Keyword(s):  
Information Technology ◽  
Optimization Problem ◽  
Data Transfer ◽  
Cost Minimization ◽  
Rapid Development ◽  
Computer Experiments ◽  
Necessary Condition ◽  
Energy Costs ◽  
Sensor Coverage ◽  
Activity Sensors

Thanks to the rapid development of technologies, in particular information, sensors have become widespread and used in all areas of human activity. Sensors and sensor networks have received special use during the collection and processing of data of various types. When monitoring a certain territory, the problem arises of its maximum coverage in order to increase the information content and completeness of the accumulated data. Simultaneously with the predominance of autonomous use of sensors, the problem of the duration of the sensor operation arises. This value depends on the capacity of the battery. In turn, engineers are faced with the task of minimizing the design of the sensors, which results in a decrease in the volume of the battery simultaneously with all other components. It is also obvious that as the sensor coverage radius increases, the energy consumption increases, which in turn shortens the sensor life. In addition to energy costs, the article considers the costs of servicing and purchasing sensors. Thus, in addition to maximizing the percentage of coverage of the study area, the problem of minimizing the total costs arises. Obviously, to ensure data transfer between sensors, a necessary condition is the presence of the intersection of the sensor coverage areas. In this case, the constant value of this parameter is considered. The materials propose an approach to solving the problem of maximizing the coverage of the territory with minimizing costs for a given level of intersection of the coverage areas of the sensors. The proposed approach is based on solving a nonlinear multiobjective optimization problem. Also, one of the options for solving the described problem is proposed to reduce the objective functions in one by using a weighted convolution of criteria. In addition, the article proposes an iterative approach to solving the described problem. A number of computer experiments have been carried out. The results of the performed computational experiments confirm the possibility of using the proposed information technology both in the form of an optimization problem and in the form of an iterative process.

Monotonicity Analysis of Taguchi’s Robust Circuit Design Problem

1990 ◽  
Author(s):  
Douglass J. Wilde
Keyword(s):  
Circuit Design ◽  
Design Problem ◽  
Recent Article ◽  
Optimization Problem ◽  
Algebraic Function ◽  
Necessary Condition ◽  
Control Range ◽  
Design Variables ◽  
Numerical Iteration ◽  
Monotonicity Analysis

Abstract A recent article showed how to formulate Taguchi’s robust circuit design problem rigorously as an optimization problem. A necessary condition for optimality was found to be that the control range be centered about the target value. This generates a constraint on the two design variables which cannot be solved for either variable. The present article shows that by approximating this unsolvable constraint with a simpler constraint that is solvable, one variable can be eliminated and the problem reduced to an unconstrained one in a single variable. Since this reduced objective turns out to be monotonic in the remaining design variable, its optimum value must be at the limit of its range. The corresponding optimum value of the other variable is then determined exactly from the true, not approximate, constraint. Since no model construction, experimentation, statistical analysis or numerical iteration is needed, this procedure is recommended whenever the input-output relation is known to be a monotonic algebraic function.

scholarly journals Minimum principle and controllability for multiparameter discrete inclusions via derived cones

2006 ◽  
Vol 2006 ◽  
pp. 1-12
Author(s):  
Aurelian Cernea
Keyword(s):  
Optimization Problem ◽  
Minimum Principle ◽  
Sufficient Conditions ◽  
Reachable Set ◽  
Local Controllability ◽  
Reference Trajectory ◽  
Endpoint Constraints ◽  
Discrete Inclusion

We consider a multiparameter discrete inclusion and we prove that the reachable set of a certain variational multiparameter discrete inclusion is a derived cone in the sense of Hestenes to the reachable set of the discrete inclusion. This result allows to obtain sufficient conditions for local controllability along a reference trajectory and a new proof of the minimum principle for an optimization problem given by a multiparameter discrete inclusion with endpoint constraints.

scholarly journals Optimization of Bridge Crane Movement Control

2018 ◽  
Vol 17 (5) ◽  
pp. 413-420
Author(s):  
V. S. Loveikin ◽  
Y. A. Romasevich
Keyword(s):  
Electric Drive ◽  
Optimization Problem ◽  
Dynamic Properties ◽  
Analytical Form ◽  
Energy Performance ◽  
Suboptimal Control ◽  
Electrical Performance ◽  
Necessary Condition ◽  
Bridge Crane ◽  
Phase Coordinates

Transient modes of bridge cranes movement determine their energy, dynamic and electrical performance, as well as productivity and durability of work. An optimal control problem of its movement has been solved while making an analysis of indicators for efficient performance of a bridge crane. Terminal and integral criteria have been selected as optimization criteria. They represent undesirable dynamic properties of the crane. Legendre method has been used to determine the possibility for achieving minimum of the optimization criterion. An analysis of the Euler-Poisson equation, which is a necessary condition for the minimum of the integral criterion, has shown that it is impossible to find a solution for the optimization problem in an analytical form. A method of differential evolution has been used in order to find an approximate solution to the optimization problem. The approximate (suboptimal) solution has been found in the complex domain, which is a limited domain conjunction of dynamic parameters and phase coordinates of the system. Limitation in the domain of the system phase coordinates (a polynomial basis function has been used in the paper) provides the possibility to attain absolute minimums of terminal problem criteria. A simulation of the bridge crane motion has been carried out in order to establish an efficiency for implementation of the suboptimal control. During this process dynamic mechanical characteristics of its electric drive have been taken into account. While carrying out the simulation, a frequency and an amplitude of the electric drive voltage in the crane movement mechanism have been changed (frequency scalar method for speed changing of an asynchronous electric drive has been used). A comparative analysis of the dynamic, kinematic, electrical and energy performance indicators of the bridge crane under suboptimal and S-curved (standard) laws of frequency and voltage variations in the crane electric drive has made it possible to establish an improvement in the efficiency of its operation under suboptimal control.

Monotonicity Analysis of Taguchi’s Robust Circuit Design Problem

1992 ◽  
Vol 114 (4) ◽  
pp. 616-619 ◽  
Author(s):  
D. J. Wilde
Keyword(s):  
Circuit Design ◽  
Design Problem ◽  
Optimization Problem ◽  
Algebraic Function ◽  
The Other ◽  
Necessary Condition ◽  
Control Range ◽  
Design Variables ◽  
Numerical Iteration ◽  
Monotonicity Analysis

Taguchi’s robust circuit design problem can be formulated rigorously as an optimization problem. A necessary condition for optimality is that the control range be centered about the target value. This generates a constraint on the two design variables which cannot be solved for either variable. The present article shows that by approximating this unsolvable constraint with a simpler constraint that is solvable, one variable can be eliminated and the problem reduced to an unconstrained one in a single variable. Since this reduced objective turns out to be monotonic in the remaining design variable, its optimum value must be at the limit of its range. The corresponding optimum value of the other variable is then determined exactly from the true, not approximate, constraint. Since no model construction, experimentation, statistical analysis, or numerical iteration is needed, this procedure is recommended whenever the input-output relation is known to be a monotonic algebraic function.

scholarly journals Data-Driven Self-Optimizing Control: Unconstrained Optimization Problem

2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Alhaji S Grema ◽  
Yi Cao ◽  
Modu B Grema
Keyword(s):  
Finite Difference ◽  
Unconstrained Optimization ◽  
Optimization Problem ◽  
Difference Schemes ◽  
Necessary Condition ◽  
Finite Difference Schemes ◽  
Central Difference ◽  
Unconstrained Optimization Problem ◽  
Optimizing Control ◽  
Necessary Condition Of Optimality

Controlled variable (CV) selection plays an important role in determining the performance of a process plant. Existing methods for CV selection through self-optimizing control requires linearization of rigorous models around nominal operating points. This is a very difficult task which results to large losses. This work presents a novel method for CV design. A necessary condition of optimality (NCO) was proposed to be the CV. The approach does not require the analytical expression of the NCO to be derived but is approximated through a single regression step based on data. Finite difference was used to approximate the NCO (gradient) using data; three finite difference schemes were employed for this purpose, which are forward, backward and central differences. Seven different cases with respect to number of sampling points, neighborhood points and finite difference schemes were investigated. To demonstrate the efficacy of the method in simplest way, it is applied to a hypothetical unconstrained optimization problem. The proposed method was found to have outperformed some existing approaches in many instances. A zero loss was recorded by some designed CVs. Central difference was found to be the best schemes among the three. Keywords— controlled variable, disturbance, finite difference, monotonicity, regression. 

scholarly journals On optimality conditions for robust weak sharp solution in uncertain optimizations

2020 ◽  
Vol 36 (3) ◽  
pp. 443-452
Author(s):  
JUTAMAS KERDKAEW ◽  
RABIAN WANGKEEREE ◽  
GUE MYUNG LEE
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Constraint Qualification ◽  
Generalized Convexity ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Robust Version ◽  
Robust Optimization Problem ◽  
Weak Sharp Solution ◽  
Weak Sharp

In this paper, we investigate the robust optimization problem involving nonsmooth and nonconvex real-valued functions. We firstly establish a necessary condition for the local robust weak sharp solution of considered problem under a constraint qualification. These optimality conditions are presented in terms of multipliers and Mordukhovich subdifferentials of the related functions. Then, by employing the robust version of the (KKT) condition, and some appropriate generalized convexity conditions, we also obtain some sufficient conditions for the global robust weak sharp solutions of the problem. In addition, some examples are presented for illustrating or supporting the results.

scholarly journals On optimality for Mayer type problem governed by a discrete inclusion system with Lipschitzian set-valued mappings

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2333-2340
Author(s):  
Özkan Değer
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Applied Mathematics ◽  
Necessary Condition ◽  
Tangent Cones ◽  
Type Problem ◽  
Local Approximations ◽  
Set Valued Mappings ◽  
Discrete Inclusion ◽  
Lower Derivative

Set-valued optimization which is an extension of vector optimization to set-valued problems is a growing branch of applied mathematics. The application of vector optimization technics to set-valued problems and the investigation of optimality conditions has been of enormous interest in the research of optimization problems. In this paper we have considered a Mayer type problem governed by a discrete inclusion system with Lipschitzian set-valued mappings. A necessary condition for K-optimal solutions of the problem is given via local approximations which is considered the lower and upper tangent cones of a set and the lower derivative of the set-valued mappings.

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