scholarly journals Strongly and Semi Strongly E_h-b-Vex Functions: Applications to Optimization Problems

2019 ◽  
pp. 2022-2029
Author(s):  
Saba Nasser Majeed
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Convex Functions ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Nonlinear Optimization Problem ◽  
Optimality Properties

In this paper, we propose new types of non-convex functions called strongly --vex functions and semi strongly --vex functions. We study some properties of these proposed functions. As an application of these functions in optimization problems, we discuss some optimality properties of the generalized nonlinear optimization problem for which we use, as an objective function, strongly --vex function and semi strongly --vex function.

scholarly journals DETERMINATION OF RHEOLOGICAL PARAMETERS OF POLYMERIC MATERIALS USING NONLINEAR OPTIMIZATION METHODS

2020 ◽  
Vol 3 (5) ◽  
pp. 15-23
Author(s):  
S. Yazyev ◽  
A. Chepurnenko ◽  
S. Litvinov
Keyword(s):  
Objective Function ◽  
Nonlinear Optimization ◽  
Creep Curve ◽  
Optimization Problem ◽  
Pure Shear ◽  
Polymeric Materials ◽  
Rheological Parameters ◽  
Rheological Characteristics ◽  
Nonlinear Optimization Problem ◽  
Creep Curves

The article is devoted to the problem of processing the experimental creep curves of polymers. The task is to determine their rheological characteristics from tests for any of the simplest types of deformation. The basis for the approximation of the experimental curves is the nonlinear Maxwell-Gurevich equation. The task of finding the rheological parameters of the material is posed as a nonlinear optimization problem. The objective function is the sum of the squared deviations of the experimental values on the creep curve from the theoretical ones. Variable input parameters of the objective function are the initial relaxation viscosity and velocity modulus m*. A theoretical creep curve is constructed numerically using the fourth-order Runge-Kutta method. The nonlinear optimization problem is solved in the Matlab environment using the internal point method. The values m* and are found for which the objective function takes the minimum value. To test the technique, the inverse problem was solved. For given values of the rheological parameters of the material, a theoretical curve of creep under bending was constructed, and the values m* and were found from it. The technique was also tested on experimental stress relaxation curves of secondary polyvinyl chloride and creep curves of polyurethane foam with a pure shear. A higher quality approximation of experimental curves is shown in comparison with existing methods. The developed technique allows us to determine the rheological characteristics of materials from tests for bending, central tension (compression), torsion, shear, and it is enough to test only one type of deformation, and not a series, as was suggested earlier by some researchers

Schedule-Constrained Demand Management in Two-Region Urban Networks

2021 ◽  
Author(s):  
Sakitha Kumarage ◽  
Mehmet Yildirimoglu ◽  
Mohsen Ramezani ◽  
Zuduo Zheng
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Time Window ◽  
Demand Management ◽  
Urban Traffic ◽  
Fundamental Diagram ◽  
Constrained System ◽  
Nonlinear Optimization Problem ◽  
Management Platform ◽  
User Compliance

Demand management aiming to optimize system cost while ensuring user compliance in an urban traffic network is a challenging task. This paper introduces a cooperative demand redistribution strategy to optimize network performance through the retiming of departure times within a limited time window. The proposed model minimizes the total time spent in a two-region urban network by incurring minimal disruption to travelers’ departure schedules. Two traffic models based on the macroscopic fundamental diagram (MFD) are jointly implemented to redistribute demand and analyze travelers’ reaction. First, we establish equilibrium conditions via a day-to-day assignment process, which allows travelers to find their preferred departure times. The trip-based MFD model that incorporates individual traveler attributes is implemented in the day-to-day assignment, and it is conjugated with a network-level detour ratio model to incorporate the effect of congestion in individual traveler route choice. This allows us to consider travelers with individual preferences on departure times influenced by desired arrival times, trip lengths, and earliness and lateness costs. Second, we develop a nonlinear optimization problem to minimize the total time spent considering both observed and unobserved demand—that is, travelers opting in and out of the demand management platform. The accumulation-based MFD model that builds on aggregated system representation is implemented as part of the constraints in the nonlinear optimization problem. The results confirm the resourcefulness of the model to address complex two-region traffic dynamics and to increase overall performance by reaching a constrained system optimum scenario while ensuring the applicability at both full and partial user compliance conditions.

scholarly journals METHODS OF FORMULATING AND SOLVING OPTIMIZATION PROBLEMS OF CUTTING LOGS OF LARGE SIZE BY BAR-SAWING METHOD WITH CUTTING OUT ONE BAR AND FIVE PAIRS OF SIDE EDGING BOARDS WITH SUBSEQUENT SAWING LUMBER FOR EDGED BOARDS

2017 ◽  
Vol 7 (1) ◽  
pp. 137-150
Author(s):  
Агапов ◽  
Aleksandr Agapov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Target Function ◽  
Cross Sectional ◽  
Optimization Task ◽  
Cutting Out ◽  
The Mathematical Model ◽  
The Relationship

For the first time the mathematical model of task optimization for this scheme of cutting logs, including the objective function and six equations of connection. The article discusses Pythagorean area of the logs. Therefore, the target function is represented as the sum of the cross-sectional areas of edging boards. Equation of the relationship represents the relationship of the diameter of the logs in the vertex end with the size of the resulting edging boards. This relationship is described through the use of the Pythagorean Theorem. Such a representation of the mathematical model of optimization task is considered a classic one. However, the solution of this mathematical model by the classic method is proved to be problematic. For the solution of the mathematical model we used the method of Lagrange multipliers. Solution algorithm to determine the optimal dimensions of the beams and side edging boards taking into account the width of cut is suggested. Using a numerical method, optimal dimensions of the beams and planks are determined, in which the objective function takes the maximum value. It turned out that with the increase of the width of the cut, thickness of the beam increases and the dimensions of the side edging boards reduce. Dimensions of the extreme side planks to increase the width of cut is reduced to a greater extent than the side boards, which are located closer to the center of the log. The algorithm for solving the optimization problem is recommended to use for calculation and preparation of sawing schedule in the design and operation of sawmill lines for timber production. When using the proposed algorithm for solving the optimization problem the output of lumber can be increased to 3-5 %.

scholarly journals Design of SkSP-R Variables Sampling Plans

2015 ◽  
Vol 38 (2) ◽  
pp. 413-429 ◽  
Author(s):  
Muhammad Aslam ◽  
Saminathan Balamurali ◽  
Chi-Hyuck Jun ◽  
Batool Hussain
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Sampling Plan ◽  
Producer’S Risk ◽  
Sample Number ◽  
Sampling Plans ◽  
Average Sample Number ◽  
Nonlinear Optimization Problem ◽  
Better Than ◽  
Average Sample

In this paper, we present the designing of the skip-lot sampling plan including the re-inspection  called SkSP-R. The plan parameters of the proposed plan are determined through a  nonlinear optimization problem by minimizing the average sample number satisfying both the producer's risk and the consumer's risks. The proposed plan is shown to perform better than the existing sampling plans in terms of the average sample number. The application of the proposed plan is explained with the help of illustrative examples.

Modeling and Identification of a Class of Servomechanism Systems With Stick-Slip Friction

1988 ◽  
Vol 110 (3) ◽  
pp. 324-328 ◽  
Author(s):  
Ka C. Cheok ◽  
Hongxing Hu ◽  
Nan K. Loh
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Optimization Procedure ◽  
Simplex Algorithm ◽  
Identification Algorithm ◽  
Stick Slip ◽  
Process Identification ◽  
Nonlinear Optimization Problem ◽  
System Parameters ◽  
Input Signals

This paper describes a technique for modeling and identifying a class of nonlinear servomechanism systems with stick-slip friction. The physics of the stick-slip friction is considered in modeling the process. Identification of the system parameters is formulated as a nonlinear optimization problem. A modified simplex algorithm is proposed as the optimization procedure. The difficulties encountered in choosing identification algorithm and input signals for the problem are discussed. A simulation example of a servomotor system is provided.

OO-Based STATCOM Installation for Power System Loading Margin Improvement

2013 ◽  
Vol 284-287 ◽  
pp. 1087-1093 ◽  
Author(s):  
Ya Chin Chang ◽  
Rung Fang Chang
Keyword(s):  
Power Systems ◽  
Power System ◽  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Transmission System ◽  
Exact Method ◽  
Ordinal Optimization ◽  
Static Synchronous Compensator ◽  
Nonlinear Optimization Problem ◽  
Voltage Instability

As electricity demands and power transactions continuously increase, it becomes vulnerable to voltage instability for power systems, generally incurred by over-utilized facilities or any contingency. The transmission system loading margin (LM) enhancement problem with Static Synchronous Compensator (STATCOM) installation can be formulated as a mixed discrete-continuous nonlinear optimization problem (MDCP); due to the complexity of the MDCP, the computing burden might be very heavy. In the paper, the proposed ordinal optimization (OO) based STATCOM installation method is applied to the MDCP to solve for good enough solutions rather than the best solution, so as to largely reduce the computation burden. In the method, the crude method is first used to solve the MDCP and, based on OO theory, the exact method is then used to determine the good enough solutions. Finally, the good enough solution, as uses the fewest STATCOM device units for installation and makes the power system able to provide the required LM, is recommended for network reinforcement.

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