A Sequential-Quadratic-Programming Algorithm Using Orthogonal Decomposition With Gerschgorin Stabilization

1999 ◽  
Vol 123 (4) ◽  
pp. 501-509 ◽  
Author(s):  
C.-P. Teng ◽  
J. Angeles
Keyword(s):  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Hessian Matrix ◽  
Initial Guess ◽  
Orthogonal Decomposition ◽  
Programming Algorithm ◽  
New Approach ◽  
Novel Approach ◽  
Programming Solution ◽  
Sequential Quadratic Programming Algorithm

This paper introduces a new approach to sequential quadratic programming. Upon application of the orthogonal-decomposition algorithm and the Gerschgorin Theorem for the stabilization of the Hessian matrix in the quadratic-programming solution, this novel approach offers an alternative to existing methods that, additionally, dispenses with a feasible initial guess.

A Sequential-Quadratic-Programming Algorithm Using Orthogonal Decomposition With Gerschgorin Stabilization

1999 ◽  
Author(s):  
Chin-Pun Teng ◽  
Jorge Angeles
Keyword(s):  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Hessian Matrix ◽  
Initial Guess ◽  
Orthogonal Decomposition ◽  
Programming Algorithm ◽  
New Approach ◽  
Novel Approach ◽  
Programming Solution ◽  
Sequential Quadratic Programming Algorithm

Abstract This paper introduces a new approach to sequential quadratic programming. Upon application of the Gerschgorin Theorem for the stabilization of the Hessian matrix and of the orthogonal-decomposition algorithm in the quadratic programming solution, this novel approach offers a faster computation and dispenses with a feasible initial guess.

scholarly journals A new geometry-based secondary path planning for automatic parking

2020 ◽  
Vol 17 (3) ◽  
pp. 172988142093057
Author(s):  
Ren-Fang Zhou ◽  
Xiao-Feng Liu ◽  
Guo-Ping Cai
Keyword(s):  
Path Planning ◽  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Programming Algorithm ◽  
Optimal Parameters ◽  
Automatic Parking ◽  
Straight Lines ◽  
Fine Tune ◽  
Sequential Quadratic Programming Algorithm ◽  
Path Tracking Algorithm

In auto-parking systems, a certain degree of error in the path tracking algorithm is inevitable. This is caused by actuator error, tire slipping, or other factors relevant to and included in the parking process. In such situations, the parking path needs to be updated to finish parking successfully which is referred to as secondary path planning. Herein, a new geometry-based method is proposed to deal with this issue, which can be called the pattern-based method. In this method, a predefined path pattern set consisting of 24 multi-segment patterns is developed first. These patterns are composed of straight lines and arcs and account for constraints due to motion and the immediate environment. Then, a traversal policy is adopted to select the path pattern from the set, and the sequential quadratic programming algorithm is used to determine the optimal parameters that fine-tune the pattern to meet the current constraints. In the simulation section, the effectiveness of the proposed method is demonstrated. Moreover, compared to the search-based method represented by a variation of rapidly exploring random tree*, the proposed method has a higher planning performance.

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