An Investigation of Pshenichnyi’s Recursive Quadratic Programming Method for Engineering Optimization

1987 ◽  
Vol 109 (2) ◽  
pp. 248-253 ◽  
Author(s):  
G. A. Gabriele ◽  
T. J. Beltracchi
Keyword(s):  
Quadratic Programming ◽  
Optimization Problems ◽  
Programming Algorithm ◽  
Test Problems ◽  
Engineering Optimization ◽  
Active Set ◽  
Original Algorithm ◽  
Recursive Quadratic Programming ◽  
Modified Algorithm ◽  
Engineering Optimization Problems

This paper discusses Pshenichnyi’s recursive quadratic programming algorithm for use in engineering optimization problems. An evaluation of the original algorithm is offered and several modifications are presented. The modifications include; addition of a variable metric update of the Hessian, an improved active set criterion, direct inclusion of the variable bounds, a divergence control mechanism, and updating schemes for the algorithm parameters. Implementations of the original algorithm and the modified algorithm were tested against the Sandgren test set of 23 engineering optimization problems. The results indicate that the modified algorithm was able to solve 20 of the 23 test problems while the original algorithm solved only 11. The modified algorithm was more efficient than the original on all the test problems.

scholarly journals An active set sequential quadratic programming algorithm for nonlinear optimisation

2006 ◽  
Vol 74 (1) ◽  
pp. 69-83
Author(s):  
Qing-Jie Hu ◽  
Yun-Hai Xiao ◽  
Y. Chen
Keyword(s):  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Least Square ◽  
Programming Algorithm ◽  
Active Set ◽  
Nonlinear Inequality ◽  
Nonlinear Inequality Constraints ◽  
Sequential Quadratic Programming Algorithm

In this paper, we have proposed an active set feasible sequential quadratic programming algorithm for nonlinear inequality constraints optimization problems. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving a reduced quadratic programming subproblem. To overcome the Maratos effect, a higher-order correction direction is obtained by solving a reduced least square problem. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without strict complementarity.

A Hybrid Variable Metric Update for the Recursive Quadratic Programming Method

1989 ◽  
Author(s):  
T. J. Beltracchi ◽  
G. A. Gabriele
Keyword(s):  
Quadratic Programming ◽  
Optimization Problems ◽  
Engineering Optimization ◽  
Variable Metric ◽  
Hybrid Variable ◽  
Recursive Quadratic Programming ◽  
Rank One ◽  
Sensitivity Studies ◽  
Symmetric Rank One ◽  
Quadratic Programming Method

Abstract The Recursive Quadratic Programming (RQP) method has been shown to be one of the most effective and efficient algorithms for solving engineering optimization problems. The RQP method uses variable metric updates to build approximations of the Hessian of the Lagrangian. If the approximation of the Hessian of the Lagrangian converges to the true Hessian of the Lagrangian, then the RQP method converges quadratically. The convergence of the Hessian approximation is affected by the choice of the variable metric update. Most of the research that has been performed with the RQP method uses the Broyden Fletcher Shanno (BFS) or Symmetric Rank One (SR1) variable metric update. The SR1 update has been shown to yield better estimates of the Hessian of the Lagrangian than those found when the BFS update is used, though there are cases where the SR1 update becomes unstable. This paper describes a hybrid variable metric update that is shown to yield good approximations of the Hessian of the Lagrangian. The hybrid update combines the best features of the SRI and BFS updates and is more stable than the SR1 update. Testing of the method shows that the efficiency of the RQP method is not affected by the new update, but more accurate Hessian approximations are produced. This should increase the accuracy of the solutions and provide more reliable information for post optimality analyses, such as parameter sensitivity studies.

scholarly journals Relaxed gradient projection algorithm for constrained node-based shape optimization

2021 ◽  
Author(s):  
Ihar Antonau ◽  
Majid Hojjat ◽  
Kai-Uwe Bletzinger
Keyword(s):  
Shape Optimization ◽  
Optimization Problems ◽  
Gradient Projection ◽  
Projection Algorithm ◽  
Design Parameters ◽  
Active Set ◽  
Physical Constraints ◽  
Original Algorithm ◽  
Gradient Projection Algorithm ◽  
Non Linear

AbstractIn node-based shape optimization, there are a vast amount of design parameters, and the objectives, as well as the physical constraints, are non-linear in state and design. Robust optimization algorithms are required. The methods of feasible directions are widely used in practical optimization problems and know to be quite robust. A subclass of these methods is the gradient projection method. It is an active-set method, it can be used with equality and non-equality constraints, and it has gained significant popularity for its intuitive implementation. One significant issue around efficiency is that the algorithm may suffer from zigzagging behavior while it follows non-linear design boundaries. In this work, we propose a modification to Rosen’s gradient projection algorithm. It includes the efficient techniques to damp the zigzagging behavior of the original algorithm while following the non-linear design boundaries, thus improving the performance of the method.

scholarly journals Improved Salp Swarm Algorithm with Simulated Annealing for Solving Engineering Optimization Problems

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1092
Author(s):  
Qing Duan ◽  
Lu Wang ◽  
Hongwei Kang ◽  
Yong Shen ◽  
Xingping Sun ◽  
...  
Keyword(s):  
Simulated Annealing ◽  
Optimization Problems ◽  
Chaotic Sequence ◽  
Engineering Optimization ◽  
Exploration And Exploitation ◽  
Salp Swarm Algorithm ◽  
Symmetric Perturbation ◽  
Swarm Algorithm ◽  
Search Capability ◽  
Engineering Optimization Problems

Swarm-based algorithm can successfully avoid the local optimal constraints, thus achieving a smooth balance between exploration and exploitation. Salp swarm algorithm(SSA), as a swarm-based algorithm on account of the predation behavior of the salp, can solve complex daily life optimization problems in nature. SSA also has the problems of local stagnation and slow convergence rate. This paper introduces an improved salp swarm algorithm, which improve the SSA by using the chaotic sequence initialization strategy and symmetric adaptive population division. Moreover, a simulated annealing mechanism based on symmetric perturbation is introduced to enhance the local jumping ability of the algorithm. The improved algorithm is referred to SASSA. The CEC standard benchmark functions are used to evaluate the efficiency of the SASSA and the results demonstrate that the SASSA has better global search capability. SASSA is also applied to solve engineering optimization problems. The experimental results demonstrate that the exploratory and exploitative proclivities of the proposed algorithm and its convergence patterns are vividly improved.

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.

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