scholarly journals LINEARIZED REQUIRED OPTIMALITY CONDITIONS IN ONE SMOOTH GURSA-DARBU SYSTEM MANAGEMENT PROBLEM

2020 ◽  
pp. 20-33
Author(s):  
Govkhar Ramazanova ◽  
Keyword(s):  
Optimality Condition ◽  
Minimax Problem ◽  
System Management ◽  
Management Problem ◽  
Necessary Optimality Condition ◽  
Control Vector ◽  
Bounded Control ◽  
Differentiable Functions ◽  
Darboux System ◽  
The Right

In class measurable (in Lebesgue sense) and bounded control vector functions, we consider one non-smooth optimal control problem of the Goursat – Darboux system with a multipoint quality functional, which is a generalization terminal type functional. Applying one modified version of the increment method, and assuming that the right side of the equation and the functional qualities in a vector state have derivatives in any direction, the necessary optimality condition in derivative terms in the direction flax general is proved. The case of a quasidifferentiable quality functional is considered. In particular, the minimax problem is studied. Under the assumption that the control region is convex, taking into account the properties of non-differentiable functions, the necessary optimality condition is established, which is an analog of the linearized integral principle of maximin, which is constructive in nature and generalizes the point wise linearized (differential) maximum principle.

Optimality of Approximate Quasi-Weakly Efficient Solutions for Vector Equilibrium Problems via Convexificators

2021 ◽  
Author(s):  
Guolin Yu ◽  
Siqi Li ◽  
Xiao Pan ◽  
Wenyan Han
Keyword(s):  
Optimality Condition ◽  
Generalized Convexity ◽  
Equilibrium Problems ◽  
Efficient Solutions ◽  
Sufficient Optimality Condition ◽  
Necessary Optimality Condition ◽  
Weakly Efficient Solutions ◽  
Convexity Assumption ◽  
Pseudoconvex Function ◽  
Vector Equilibrium

This paper is devoted to the investigation of optimality conditions for approximate quasi-weakly efficient solutions to a class of nonsmooth Vector Equilibrium Problem (VEP) via convexificators. First, a necessary optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is presented by making use of the properties of convexificators. Second, the notion of approximate pseudoconvex function in the form of convexificators is introduced, and its existence is verified by a concrete example. Under the introduced generalized convexity assumption, a sufficient optimality condition for approximate quasi-weakly efficient solutions to problem (VEP) is also established. Finally, a scalar characterization for approximate quasi-weakly efficient solutions to problem (VEP) is obtained by taking advantage of Tammer’s function.

scholarly journals A note on the paper "Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming"

2020 ◽  
Author(s):  
Nazih Abderrazzak Gadhi ◽  
Aissam Ichatouhane
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Optimality Condition ◽  
Short Proof ◽  
Necessary Optimality Condition ◽  
Main Result Theorem ◽  
Correct Formulation ◽  
Result Theorem ◽  
Infinite Programming ◽  
Interval Valued

A nonsmooth semi-infinite interval-valued vector programming problem is solved in the paper by Jennane et all. (RAIRO-Oper. Res. doi: 10.1051/ro/2020066, 2020). The necessary optimality condition obtained by the authors, as well as its proof, is false. Some counterexamples are given to refute some results on which the main result (Theorem 4.5) is based. For the convinience of the reader, we correct the faulty in those results, propose a correct formulation of Theorem 4.5 and give also a short proof.

scholarly journals Necessary optimality condition for trilevel optimization problem

2020 ◽  
Vol 16 (1) ◽  
pp. 55-70
Author(s):  
Gaoxi Li ◽  
◽  
Zhongping Wan ◽  
Jia-wei Chen ◽  
Xiaoke Zhao ◽  
...  
Keyword(s):  
Optimality Condition ◽  
Optimization Problem ◽  
Necessary Optimality Condition

scholarly journals A Hybrid Approach of VIKOR and Bi-Objective Decision Model for Emergency Shelter Location–Allocation to Respond to Earthquakes

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1897
Author(s):  
Shaoqing Geng ◽  
Hanping Hou ◽  
Zhou Zhou
Keyword(s):  
Hybrid Approach ◽  
Capacity Utilization ◽  
Management Problem ◽  
Emergency Shelter ◽  
Location Allocation ◽  
Disaster Relief Operations ◽  
Allocation Process ◽  
The Government ◽  
The Right ◽  
The Impact

Earthquakes have catastrophic effects on the affected population, especially in undeveloped countries or regions. Minimizing the impact and consequences of earthquakes involves many decisions and disaster relief operations that should be optimized. A critical disaster management problem is to construct shelters with reasonable capacity in the right locations, allocate evacuees, and provide relief materials to them within a reasonable period. This study proposes a bi-objective hierarchical model with two stages, namely, the temporary shelter stage and the short-term shelter stage. The proposed objectives at different stages are to minimize the evacuation time, maximize the suitability based on qualitative factors, and minimize the number of sites while considering the demand, capacity, utilization, and budget constraints. The performance evaluation of the emergency shelter was carried out by fuzzy-VIKOR, and the most ideal location of the shelter was determined through multiple standards. Emergency management organizations can benefit from the collective expertise of multiple decision-makers because the proposed method uses their knowledge to automate the location and allocation process of shelters. In the case of Chengdu, Sichuan Province, China, the results of using this hybrid approach provide the government with a range of options. This method can realize the trade-off between efficiency and cost in the emergency shelter location and material distribution, and realize reliable solutions in disaster emergencies.

scholarly journals Institutional Model in Management of Drainage System

2019 ◽  
Vol 9 (2) ◽  
pp. 1099-1103
Keyword(s):  
Flood Control ◽  
Central Government ◽  
Drainage System ◽  
System Management ◽  
Community Based ◽  
System Maintenance ◽  
Systems Maintenance ◽  
The Government ◽  
Institutional Model ◽  
The Right

Flood is a regular problem in Semarang. The causes of flooding include changes in land use, intensity and high rainfall and erosion and sedimentation in the river channel. Development efforts for flood control has been conducted, such as the development and optimization of drainage systems. Maintenance and operation of the drainage system supported by the good institutional capacity is expected to handle the problem of flooding. Therefore, the right institutional model is necessary in the management of the drainage system of Semarang. The research data were obtained through a variety of literature as well as interviews with the parties related to the management of drainage in Semarang. There was three institutional model of drainage system management implemented in Semarang were institutional model of government-based, institutional model of community-based, and institutional model of stakeholders-based. There were 24 respondents from government, municipality, entrepreneurs and communities who have assessed the institutional model of drainage system management. Each institutional model analyzed in the five aspects of drainage management, namely technical, institutional, legal, financial and community participation. The results of the study showed that the most appropriate institutional model for managing the drainage system in Semarang is institutional model of stakeholders-based. This institutional model has the advantage such as drainage system maintenance can be handled more quickly, the legal regulations issued by the government and financing sources drainage system can come from any source, such as the central government, municipalities, grants, and also from non-governmental.

Noether’s theorem for fractional variational problems of variable order

Open Physics ◽  
2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Tatiana Odzijewicz ◽  
Agnieszka Malinowska ◽  
Delfim Torres
Keyword(s):  
Optimality Condition ◽  
Variational Problems ◽  
Time Variable ◽  
Variable Order ◽  
Necessary Optimality Condition ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Fractional Variational Problems ◽  
Derivatives Of

AbstractWe prove a necessary optimality condition of Euler-Lagrange type for fractional variational problems with derivatives of incommensurate variable order. This allows us to state a version of Noether’s theorem without transformation of the independent (time) variable. Considered derivatives of variable order are defined in the sense of Caputo.

scholarly journals A multiplier rule in set-valued optimisation

2003 ◽  
Vol 68 (1) ◽  
pp. 93-100 ◽  
Author(s):  
Akhtar A. Khan ◽  
Fabio Raciti
Keyword(s):  
Optimality Condition ◽  
Necessary Optimality Condition ◽  
Dini Derivative ◽  
Multiplier Rule

A multiplier rule is given as a necessary optimality condition for proper minimality in set-valued optimisation. We use derivatives in the sense of the lower Dini derivative for the objective set-valued map and the set-valued maps defining the constraints.

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