On the quadratic programming algorithm of Goldfarb and Idnani

1985 ◽  
pp. 46-61 ◽  
Author(s):  
M. J. D. Powell
Keyword(s):  
Quadratic Programming ◽  
Programming Algorithm

Optimization With Discrete Variables Via Recursive Quadratic Programming: Part 2—Algorithm and Results

1989 ◽  
Vol 111 (1) ◽  
pp. 130-136 ◽  
Author(s):  
J. Z. Cha ◽  
R. W. Mayne
Keyword(s):  
Quadratic Programming ◽  
Performance Comparison ◽  
Programming Algorithm ◽  
Discrete Variables ◽  
Contour Analysis ◽  
Recursive Quadratic Programming ◽  
Analysis Technique ◽  
Rank One ◽  
Symmetric Rank One ◽  
Monotonicity Analysis

A discrete recursive quadratic programming algorithm is developed for a class of mixed discrete constrained nonlinear programming (MDCNP) problems. The symmetric rank one (SR1) Hessian update formula is used to generate second order information. Also, strategies, such as the watchdog technique (WT), the monotonicity analysis technique (MA), the contour analysis technique (CA), and the restoration of feasibility have been considered. Heuristic aspects of handling discrete variables are treated via the concepts and convergence discussions of Part I. This paper summarizes the details of the algorithm and its implementation. Test results for 25 different problems are presented to allow evaluation of the approach and provide a basis for performance comparison. The results show that the suggested method is a promising one, efficient and robust for the MDCNP problem.

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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