Log-sum-exp Optimization based on Continuous Piecewise Linearization Techniques

2020 ◽  
Author(s):  
Xiangming Xi ◽  
Jun Xu ◽  
Yunjiang Lou
Keyword(s):  
Piecewise Linearization ◽  
Linearization Techniques

Optimal Design of a Speed Reducer

2013 ◽  
Vol 376 ◽  
pp. 327-330 ◽  
Author(s):  
Ming Hua Lin ◽  
Jung Fa Tsai
Keyword(s):  
Mathematical Model ◽  
Optimal Design ◽  
Design Problem ◽  
Geometric Programming ◽  
Deterministic Approach ◽  
Piecewise Linearization ◽  
Design Problems ◽  
Speed Reducer ◽  
The Mathematical Model ◽  
Linearization Techniques

The mathematical model for optimal design of a speed reducer is a generalized geometric programming problem that is non-convex and not easy be globally solved. This paper applies a deterministic approach including convexification strategies and piecewise linearization techniques to globally solve speed reducer design problems. A practical speed reducer design problem is solved to demonstrate that this study obtains a better solution than other methods.

scholarly journals Piecewise Linearization for Solving Models to Locate Urban Logistics Facilities

2020 ◽  
Vol 53 (2) ◽  
pp. 11181-11186
Author(s):  
Jelibeth Racedo-Gutiérrez ◽  
Fidel Torres-Delgado
Keyword(s):  
Piecewise Linearization

A multivariate spectral quasi-linearization method for the solution of (2+1) dimensional Burgers’ equations

2020 ◽  
Vol 21 (7-8) ◽  
pp. 683-691
Author(s):  
Phumlani G. Dlamini ◽  
Vusi M. Magagula
Keyword(s):  
Collocation Method ◽  
Three Dimensional ◽  
Linearization Method ◽  
High Accuracy ◽  
Time Variable ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Burgers Equations ◽  
Grid Points ◽  
Linearization Techniques

AbstractIn this paper, we introduce the multi-variate spectral quasi-linearization method which is an extension of the previously reported bivariate spectral quasi-linearization method. The method is a combination of quasi-linearization techniques and the spectral collocation method to solve three-dimensional partial differential equations. We test its applicability on the (2 + 1) dimensional Burgers’ equations. We apply the spectral collocation method to discretize both space variables as well as the time variable. This results in high accuracy in both space and time. Numerical results are compared with known exact solutions as well as results from other papers to confirm the accuracy and efficiency of the method. The results show that the method produces highly accurate solutions and is very efficient for (2 + 1) dimensional PDEs. The efficiency is due to the fact that only few grid points are required to archive high accuracy. The results are portrayed in tables and graphs.

On Thick-Walled Cylinder Under Internal Pressure

2003 ◽  
Vol 125 (3) ◽  
pp. 267-273 ◽  
Author(s):  
W. Zhao ◽  
R. Seshadri ◽  
R. N. Dubey
Keyword(s):  
Internal Pressure ◽  
Strain Curve ◽  
Stress Strain ◽  
Piecewise Linearization ◽  
Elastic Plastic ◽  
Plastic Cylinder ◽  
Parametric Functions ◽  
The Difference ◽  
New Formulation ◽  
Walled Cylinder

A technique for elastic-plastic analysis of a thick-walled elastic-plastic cylinder under internal pressure is proposed. It involves two parametric functions and piecewise linearization of the stress-strain curve. A deformation type of relationship is combined with Hooke’s law in such a way that stress-strain law has the same form in all linear segments, but each segment involves different material parameters. Elastic values are used to describe elastic part of deformation during loading and also during unloading. The technique involves the use of deformed geometry to satisfy the boundary and other relevant conditions. The value of strain energy required for deformation is found to depend on whether initial or final geometry is used to satisfy the boundary conditions. In the case of low work-hardening solid, the difference is significant and cannot be ignored. As well, it is shown that the new formulation is appropriate for elastic-plastic fracture calculations.

A Least Cost Transmission Planning Model Considering Operation Cost

2014 ◽  
Vol 15 (2) ◽  
pp. 121-128
Author(s):  
Jorge Hans Alayo
Keyword(s):  
Test System ◽  
Mixed Integer ◽  
Transmission Planning ◽  
Integer Linear Programming Problem ◽  
Transmission Expansion ◽  
Planning Models ◽  
Proposed Model ◽  
Expansion Model ◽  
Operation Cost ◽  
Linearization Techniques

Abstract Existing transmission planning models consider basic aspects of the problem. In practice, a transmission utility needs to model other important details such as operation cost of the power system. In this article, a least cost transmission expansion model is proposed considering the operation cost in order to model the trade-off between building new transmission capacity and increasing the power system’s operation cost. The proposed model is transformed into a mixed integer linear programming problem using linearization techniques and solved with CPLEX. Finally, results of the model for the Garver test system and IEEE 24-bus test system are shown.

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