Node set optimization problem for complete Josephus cubes

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.

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Scalarization and convergence in unified set optimization

RAIRO - Operations Research ◽

10.1051/ro/2021169 ◽

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.

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

OF THE VIII INTERNATIONAL SCIENTIFIC AND PRACTICAL CONFERENCE «INNOVATIVE TECHNOLOGIES IN SCIENCE AND EDUCATION» («ITSE 2020» CONFERENCE) ◽

10.23947/itno.2020.47-51 ◽

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.

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OPTIMIZATION OF PARAMETERS OF GENERALIZED DISPERSION ALGORITHM AT STATISTICAL PROCESS CONTROL

Автоматизация процессов управления ◽

10.35752/1991-2927-2021-3-65-41-47 ◽

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.

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Set optimization using improvement sets

Yugoslav journal of operations research ◽

10.2298/yjor170115011d ◽

2017 ◽

Vol 27 (2) ◽

pp. 153-167 ◽

Cited By ~ 4

Author(s):

M. Dhingra ◽

C.S. Lalitha

Keyword(s):

Vector Optimization ◽

Optimization Problem ◽

Optimization Problems ◽

Existence Theorems ◽

Minimal Solution ◽

Set Optimization ◽

Vector Optimization Problems ◽

Optimal Solutions ◽

Solution Sets ◽

Improvement Sets

In this paper we introduce a notion of minimal solutions for set-valued optimization problem in terms of improvement sets, by unifying a solution notion, introduced by Kuroiwa [15] for set-valued problems, and a notion of optimal solutions in terms of improvement sets, introduced by Chicco et al. [4] for vector optimization problems. We provide existence theorems for these solutions, and establish lower convergence of the minimal solution sets in the sense of Painlev?-Kuratowski.

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