scholarly journals Stochastic Separated Continuous Conic Programming: Strong Duality and a Solution Method

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
Xiaoqing Wang
Keyword(s):  
Duality Theory ◽  
Solution Method ◽  
Optimization Problems ◽  
Strong Duality ◽  
Conic Programming ◽  
Linear Quadratic Control ◽  
Linear Quadratic ◽  
New Class ◽  
Polynomial Time Approximation Algorithm ◽  
The Relationship

We study a new class of optimization problems calledstochastic separated continuous conic programming(SSCCP). SSCCP is an extension to the optimization model calledseparated continuous conic programming(SCCP) which has applications in robust optimization and sign-constrained linear-quadratic control. Based on the relationship among SSCCP, its dual, and their discretization counterparts, we develop a strong duality theory for the SSCCP. We also suggest a polynomial-time approximation algorithm that solves the SSCCP to any predefined accuracy.

scholarly journals On the relationship between regression analysis and mathematical programming

2004 ◽  
Vol 8 (2) ◽  
pp. 131-140 ◽  
Author(s):  
Dong Qian Wang ◽  
Stefanka Chukova ◽  
C. D. Lai
Keyword(s):  
Regression Analysis ◽  
Mathematical Programming ◽  
Quadratic Programming ◽  
Operations Research ◽  
Optimization Problems ◽  
The Other ◽  
Linear Quadratic ◽  
Quadratic Programming Problems ◽  
Simplex Methods ◽  
The Relationship

The interaction between linear, quadratic programming and regression analysis are explored by both statistical and operations research methods. Estimation and optimization problems are formulated in two different ways: on one hand linear and quadratic programming problems are formulated and solved by statistical methods, and on the other hand the solution of the linear regression model with constraints makes use of the simplex methods of linear or quadratic programming. Examples are given to illustrate the ideas.

Higher order duality for cone vector optimization problems

2018 ◽  
Vol 13 (01) ◽  
pp. 2050020
Author(s):  
Vivek Singh ◽  
Anurag Jayswal ◽  
S. Al-Homidan ◽  
I. Ahmad
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Strong Duality ◽  
Vector Optimization Problem ◽  
Higher Order ◽  
Support Functions ◽  
Invex Functions ◽  
New Class ◽  
Duality Results ◽  
Higher Order Duality

In this paper, we present a new class of higher order [Formula: see text]-[Formula: see text]-invex functions over cones. Further, we formulate two types of higher order dual models for a vector optimization problem over cones containing support functions in objectives as well as in constraints and establish several duality results, viz., weak and strong duality results.

Duality Theory

1995 ◽  
Author(s):  
Christodoulos A. Floudas
Keyword(s):  
Duality Theory ◽  
Dual Problem ◽  
Optimization Problems ◽  
Strong Duality ◽  
Perturbation Function ◽  
Primal Problem ◽  
Theory Section ◽  
Existence Conditions ◽  
Definition Of ◽  
Optimal Multiplier

Nonlinear optimization problems have two different representations, the primal problem and the dual problem. The relation between the primal and the dual problem is provided by an elegant duality theory. This chapter presents the basics of duality theory. Section 4.1 discusses the primal problem and the perturbation function. Section 4.2 presents the dual problem. Section 4.3 discusses the weak and strong duality theorems, while section 4.4 discusses the duality gap. This section presents the formulation of the primal problem, the definition and properties of the perturbation function, the definition of stable primal problem, and the existence conditions of optimal multiplier vectors.

scholarly journals Duality Theorems for (ρ,ψ,d)-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 894
Author(s):  
Savin Treanţă
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Integral Functional ◽  
Multiple Integral ◽  
Control Problems ◽  
Duality Theorems ◽  
New Class ◽  
Duality Results ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated with an interval-valued multiple-integral functional, we formulate and prove weak, strong, and converse duality results for the considered class of variational control problems.

scholarly journals Service Restoring Reconfiguration for Distribution NetworksConsidering Uncertainty in Available Information

2021 ◽  
Vol 11 (9) ◽  
pp. 4169
Author(s):  
Hirotaka Takano ◽  
Junichi Murata ◽  
Kazuki Morishita ◽  
Hiroshi Asano
Keyword(s):  
Power Distribution ◽  
Solution Method ◽  
Optimization Problems ◽  
Problem Formulation ◽  
Distribution Networks ◽  
Accurate Information ◽  
Power Distribution Networks ◽  
Combinatorial Optimization Problems ◽  
Service Restoration ◽  
Available Information

The recent growth in the penetration of photovoltaic generation systems (PVs) has brought new difficulties in the operating and planning of electric power distribution networks. This is because operators of the distribution networks normally cannot monitor or control the output of the PVs, which introduces additional uncertainty into the available information that operations must rely on. This paper focuses on the service restoration of the distribution networks, and the authors propose a problem framework and its solution method that finds the optimal restoration configuration under extensive PV installation. The service restoration problems have been formulated as combinatorial optimization problems. They do, however, require accurate information on load sections, which is impractical in distribution networks with extensively installed PVs. A combined framework of robust optimization and two-stage stochastic programming adopted in the proposed problem formulation enables us to deal with the PV-originated uncertainty using readily available information only. In addition, this problem framework can be treated by a traditional solution method with slight extensions. The validity of the authors’ proposal is verified through numerical simulations on a real-scale distribution network model and includes a discussion of their results.

scholarly journals Monolayer Twisted Graphene-Based Schottky Transistor

Materials ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4109
Author(s):  
Ramin Ahmadi ◽  
Mohammad Taghi Ahmadi ◽  
Seyed Saeid Rahimian Koloor ◽  
Michal Petrů
Keyword(s):  
Dispersion Relation ◽  
Quantum Tunneling ◽  
Research Study ◽  
Channel Length ◽  
New Class ◽  
Metal Semiconductor Metal ◽  
The Relationship ◽  
Graphene Structures ◽  
Twisted Graphene ◽  
Device Technology

The outstanding properties of graphene-based components, such as twisted graphene, motivates nanoelectronic researchers to focus on their applications in device technology. Twisted graphene as a new class of graphene structures is investigated in the platform of transistor application in this research study. Therefore, its geometry effect on Schottky transistor operation is analyzed and the relationship between the diameter of twist and number of twists are explored. A metal–semiconductor–metal twisted graphene-based junction as a Schottky transistor is considered. By employing the dispersion relation and quantum tunneling the variation of transistor performance under channel length, the diameter of twisted graphene, and the number of twists deviation are studied. The results show that twisted graphene with a smaller diameter affects the efficiency of twisted graphene-based Schottky transistors. Additionally, as another main characteristic, the ID-VGS is explored, which indicates that the threshold voltage is increased by diameter and number of twists in this type of transistor.

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