On the relationship between fenchel and Lagrange duality for optimization problems in general spaces

Optimization ◽  
1985 ◽  
Vol 16 (1) ◽  
pp. 7-14 ◽  
Author(s):  
S. Dietze ◽  
M. Schäuble
Keyword(s):  
Optimization Problems ◽  
Lagrange Duality ◽  
The Relationship

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 %.

Lagrange Duality for Evenly Convex Optimization Problems

2015 ◽  
Vol 168 (1) ◽  
pp. 109-128 ◽  
Author(s):  
María D. Fajardo ◽  
Margarita M. L. Rodríguez ◽  
José Vidal
Keyword(s):  
Convex Optimization ◽  
Optimization Problems ◽  
Lagrange Duality ◽  
Convex Optimization Problems

scholarly journals Continuous-Time Multiobjective Optimization Problems via Invexity

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Valeriano A. De Oliveira ◽  
Marko A. Rojas-Medar
Keyword(s):  
Continuous Time ◽  
Efficient Solution ◽  
Multiobjective Programming ◽  
Optimization Problems ◽  
Weakly Efficient Solution ◽  
Multiobjective Problems ◽  
Multiobjective Optimization Problems ◽  
Relationship Of ◽  
The Relationship ◽  
Multiobjective Programming Problems

We introduce some concepts of generalized invexity for the continuous-time multiobjective programming problems, namely, the concepts of Karush-Kuhn-Tucker invexity and Karush-Kuhn-Tucker pseudoinvexity. Using the concept of Karush-Kuhn-Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems. Further, we show that Karush-Kuhn-Tucker pseudoinvexity is a necessary and suffcient condition for a vector Karush-Kuhn-Tucker solution to be a weakly efficient solution.

scholarly journals ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhi-Ang Zhou
Keyword(s):  
Saddle Point ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Saddle Points ◽  
Linear Spaces ◽  
Equivalent Characterization ◽  
Generalized Cone Subconvexlikeness ◽  
Real Linear ◽  
The Relationship

We studyϵ-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization ofϵ-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between theϵ-Henig saddle point of the Lagrangian set-valued map and theϵ-Henig properly efficient element of the set-valued optimization problem is presented. Finally, some duality theorems are given.

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.

A Kind of Adaptive Quantum Particle Swarm Algorithm Based on Phase Encoding

2012 ◽  
Vol 548 ◽  
pp. 612-616
Author(s):  
Jun Hui Pan ◽  
Hui Wang ◽  
Pan Chi Li
Keyword(s):  
Particle Swarm Optimization Algorithm ◽  
Optimization Problems ◽  
Quantum Particle ◽  
Particle Swarm ◽  
Particle Swarm Algorithm ◽  
Quantum Bits ◽  
Swarm Algorithm ◽  
The Relationship ◽  
Better Than ◽  
Function Extremum

To improve the optimization performance of particle swarm, an adaptive quantum particle swarm optimization algorithm is proposed. In the algorithm, the spatial position of particles is described by the phase of quantum bits, and the position mutation of particles is achieved by Pauli-Z gates. An adaptive determination method of the global-factors is proposed by studying the relationship among inertia factors, self-factors and global-factors. The experimental results demonstrate that the proposed algorithm is much better than the standard particle swarm algorithm by solving the function extremum optimization problems.

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.

scholarly journals Optimality Conditions for Group Sparse Constrained Optimization Problems

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 84
Author(s):  
Wenying Wu ◽  
Dingtao Peng
Keyword(s):  
Constrained Optimization ◽  
Optimality Conditions ◽  
Stationary Point ◽  
Tangent Cone ◽  
Optimization Problems ◽  
Stationary Points ◽  
Tangent Cones ◽  
Sufficient Optimality Conditions ◽  
Normal Cones ◽  
The Relationship

In this paper, optimality conditions for the group sparse constrained optimization (GSCO) problems are studied. Firstly, the equivalent characterizations of Bouligand tangent cone, Clarke tangent cone and their corresponding normal cones of the group sparse set are derived. Secondly, by using tangent cones and normal cones, four types of stationary points for GSCO problems are given: TB-stationary point, NB-stationary point, TC-stationary point and NC-stationary point, which are used to characterize first-order optimality conditions for GSCO problems. Furthermore, both the relationship among the four types of stationary points and the relationship between stationary points and local minimizers are discussed. Finally, second-order necessary and sufficient optimality conditions for GSCO problems are provided.

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