A recursive quadratic programming algorithm that uses differentiable exact penalty functions

1986 ◽  
Vol 35 (3) ◽  
pp. 265-278 ◽  
Author(s):  
M. J. D. Powell ◽  
Y. Yuan
Keyword(s):  
Quadratic Programming ◽  
Penalty Functions ◽  
Exact Penalty Functions ◽  
Programming Algorithm ◽  
Exact Penalty ◽  
Recursive Quadratic Programming

scholarly journals A Weighted Method for Fast Resolution of Strictly Hierarchical Robot Task Specifications Using Exact Penalty Functions

2021 ◽  
Vol 6 (2) ◽  
pp. 3057-3064
Author(s):  
Ajay Suresha Sathya ◽  
Goele Pipeleers ◽  
Wilm Decre ◽  
Jan Swevers
Keyword(s):  
Penalty Functions ◽  
Exact Penalty Functions ◽  
Exact Penalty ◽  
Robot Task ◽  
Fast Resolution

General exact penalty functions in integer programming

2004 ◽  
Vol 8 (1) ◽  
pp. 19-23
Author(s):  
Fu-sheng Bai ◽  
Lian-sheng Zhang ◽  
Zhi-you Wu
Keyword(s):  
Integer Programming ◽  
Penalty Functions ◽  
Exact Penalty Functions ◽  
Exact Penalty

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 Smoothing Approximation to the Square-Root Exact Penalty Function

2016 ◽  
Vol 4 (1) ◽  
pp. 87-96
Author(s):  
Yaqiong Duan ◽  
Shujun Lian
Keyword(s):  
Penalty Function ◽  
Original Problem ◽  
Optimal Solution ◽  
Penalty Functions ◽  
Exact Penalty Functions ◽  
Exact Penalty ◽  
Square Root ◽  
Inequality Constrained Optimization ◽  
Numerical Examples ◽  
Mild Conditions

AbstractIn this paper, smoothing approximation to the square-root exact penalty functions is devised for inequality constrained optimization. It is shown that an approximately optimal solution of the smoothed penalty problem is an approximately optimal solution of the original problem. An algorithm based on the new smoothed penalty functions is proposed and shown to be convergent under mild conditions. Three numerical examples show that the algorithm is efficient.

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