Planning Trajectories Using an Extended Sequential Linearization Algorithm

2021 ◽  
pp. 227-238
Author(s):  
Marco Sippel ◽  
Hermann Winner
Keyword(s):  
Sequential Linearization

Foraging-Directed Adaptive Linear Programming: An Algorithm for Solving Nonlinear Mixed Discrete/Continuous Design Problems

1996 ◽  
Author(s):  
Kemper Lewis ◽  
Farrokh Mistree
Keyword(s):  
Linear Programming ◽  
Continuous Variables ◽  
Design Problems ◽  
Design Studies ◽  
Design Models ◽  
Sequential Linearization ◽  
And Behavior

Abstract Design models often contain a combination of discrete, integer, and continuous variables. Previously, the Adaptive Linear Programming (ALP) Algorithm, which is based on sequential linearization, has been used to solve design models composed of continuous and Boolean variables. In this paper, we extend the ALP Algorithm using a discrete heuristic based on the analogy of an animal foraging for food. This algorithm for mixed discrete/continuous design problems integrates ALP and the foraging search and is called Foraging-directed Adaptive Linear Programming (FALP). Two design studies are presented to illustrate the effectiveness and behavior of the algorithm.

scholarly journals A new view of the Bubnov-Galerkin method in the linearization context

2012 ◽  
Vol 34 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Nguyen Dong Anh ◽  
I. Elishakoff
Keyword(s):  
Galerkin Method ◽  
Nonlinear Equations ◽  
Duffing Oscillator ◽  
Linearization Method ◽  
New Method ◽  
Equivalent Linearization ◽  
Equivalent Linearization Method ◽  
Sequential Linearization ◽  
New View

In the study an extension of the Bubnov-Galerkin method in terms of the equivalent linearization method is presented. It is combined with sequential linearization and nonlinear procedure to yield a new method for solving nonlinear equations which can improve the accuracy when the nonlinearity is strong. For illustration the Duffing oscillator is considered to show the effectiveness of the proposed method.

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