Convergence of Solutions of a Set Optimization Problem in the Image Space

2016 ◽  
Vol 170 (2) ◽  
pp. 358-371 ◽  
Author(s):  
César Gutiérrez ◽  
Enrico Miglierina ◽  
Elena Molho ◽  
Vicente Novo
Keyword(s):  
Optimization Problem ◽  
Image Space ◽  
Set Optimization ◽  
Convergence Of Solutions ◽  
Set Optimization Problem

Node set optimization problem for complete Josephus cubes

2019 ◽  
Vol 38 (4) ◽  
pp. 1180-1195
Author(s):  
Micheal Arockiaraj ◽  
Jessie Abraham ◽  
Arul Jeya Shalini
Keyword(s):  
Optimization Problem ◽  
Set Optimization ◽  
Set Optimization Problem

scholarly journals Scalarization and well-posedness for set optimization using coradiant sets

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3457-3471
Author(s):  
Bin Yao ◽  
Sheng Li
Keyword(s):  
Optimization Problem ◽  
Set Optimization ◽  
Well Posedness ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Scalar Optimization ◽  
Set Optimization Problem ◽  
Order Relations ◽  
Scalarization Function

The aim of this paper is to study scalarization and well-posedness for a set-valued optimization problem with order relations induced by a coradiant set. We introduce the notions of the set criterion solution for this problem and obtain some characterizations for these solutions by means of nonlinear scalarization. The scalarization function is a generalization of the scalarization function introduced by Khoshkhabar-amiranloo and Khorram. Moveover, we define the pointwise notions of LP well-posedness, strong DH-well-posedness and strongly B-well-posedness for the set optimization problem and characterize these properties through some scalar optimization problem based on the generalized nonlinear scalarization function respectively.

scholarly journals Scalarization and convergence  in unified set optimization

2021 ◽  
Author(s):  
Khushboo Rai ◽  
Prof. C.S. Lalitha
Keyword(s):  
Distance Function ◽  
Optimization Problem ◽  
Existence Result ◽  
Preference Relation ◽  
Minimal Solution ◽  
Set Optimization ◽  
Set Optimization Problem ◽  
Oriented Distance Function ◽  
Oriented Distance ◽  
Kuratowski Convergence

This paper deals with scalarization and stability aspects for a unified set optimization problem. We provide characterizations for a unified preference relation and the corresponding  unified minimal solution in terms of a generalized oriented distance function of the sup-inf type. We  establish continuity of a function associated with the generalized oriented distance function and provide an existence result for the unified minimal solution. We establish  Painlevé-Kuratowski convergence of  minimal solutions of a family of   scalar problems  to the minimal solutions of the unified set optimization problem.

scholarly journals DETERMINATION OF ACCEPTABLE RISK PARAMETERS FOR MATERIAL COSTS TO ENSURE THE QUALITY OF ENGINEERING PRODUCTS

2020 ◽  
Author(s):  
V.A. Vaganov ◽  
◽  
V.P. Dimitrov ◽  
I.A. Zaytseva ◽  
N.M. Kharakhashyan
Keyword(s):  
Optimization Problem ◽  
Optimal Level ◽  
Management Theory ◽  
Acceptable Risk ◽  
Analog Method ◽  
Set Optimization Problem ◽  
Material Costs ◽  
Risk Parameters

The article presents the results of research on analog methods of risk assessment. One of the variants of these methods has been developed as a tool for practical forecasting of the optimal level of material costs to ensure a given product quality. The theoretical basis for solving this problem was the provisions of the risk management theory of technical systems. The analog method of solving the set optimization problem presented in this paper confirms the principle possibility of predicting the level of acceptable risk of material costs for organizational and technical perfection of production, taking into account consumer requirements for its quality indicators.

Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation

2020 ◽  
Vol 185 (2) ◽  
pp. 416-432 ◽  
Author(s):  
Lam Quoc Anh ◽  
Tran Quoc Duy ◽  
Dinh Vinh Hien ◽  
Daishi Kuroiwa ◽  
Narin Petrot
Keyword(s):  
Optimization Problems ◽  
Order Relation ◽  
Set Optimization ◽  
Convergence Of Solutions ◽  
Set Less Order Relation

scholarly journals OPTIMIZATION OF PARAMETERS OF GENERALIZED DISPERSION ALGORITHM AT STATISTICAL PROCESS CONTROL

2021 ◽  
Vol 3 (65) ◽  
pp. 41-47
Author(s):  
Vladimir N. Klyachkin ◽  
◽  
Anastasiya V. Alekseeva ◽  
Keyword(s):  
Production Process ◽  
Optimization Problem ◽  
Unstable State ◽  
Statistical Control ◽  
Optimal Parameters ◽  
Multivariate Statistical ◽  
Statistical Process ◽  
Generalized Variance ◽  
Process Indicators ◽  
Set Optimization Problem

When monitoring a real production process using statistical methods, the question of early detection of violations arises. In most cases, several indicators are monitored simultaneously in the production process, and a change in the values of some indicators leads to a change in others. If there is a dependence of indicators for their monitoring, multivariate statistical control tools are used, in particular generalized variance chart. By varying the parameters of the chart, its efficiency can be significantly increased, this allows minimizing the time the process is in an unstable state.Applying the approach of A. Duncan, which he developed for Shewhart charts, a formula for the expectation of the duration of an unstable state of a process was obtained and a Python program was developed to minimize it. To test the set optimization problem, the calculation of the data of two process indicators is given and the optimal parameters of the generalized variance chart are obtained, at which the duration of the process in an unstable state is minimal.

scholarly journals Piecewise synergetic systems and applications in biochemical systems theory

2017 ◽  
Vol 24 (1) ◽  
pp. 135-148
Author(s):  
Arcady Ponosov ◽  
Anna Machina ◽  
Valeria Tafintseva
Keyword(s):  
Numerical Analysis ◽  
Systems Theory ◽  
Optimization Problem ◽  
Compartment Model ◽  
Steady States ◽  
Estimation Of Parameters ◽  
Convergence Of Solutions ◽  
Biochemical Systems Theory ◽  
Biochemical Systems ◽  
Theoretical And Numerical Analysis

AbstractWe study piecewise synergetic systems originating from Biochemical Systems Theory. In the first part of the paper, the emphasis is put on practical calculations with such systems. We consider four examples: calculation of trajectories and steady states, solution of an optimization problem and a method of estimation of parameters (kinetic orders), all examples being biologically motivated. In the second part of the paper, we study convergence of solutions, in particularly, steady states, of a sequence of piecewise synergetic systems approximating an arbitrary compartment model. This convergence analysis is then applied to the optimization problem and the method of estimating sensitivities (kinetic orders) in a generic compartment model. In this paper we put forward arguments for the importance of the theoretical and numerical analysis of piecewise synergetic systems.

Sign in / Sign up

Export Citation Format

Share Document