Gradient-projection and policy-iteration methods for solving optimization problems in STEOR networks

1984 ◽  
Vol 28 (3) ◽  
pp. 67-88 ◽  
Author(s):  
P. N. Delivorias ◽  
K. Neumann ◽  
U. Steinhardt
Keyword(s):  
Optimization Problems ◽  
Policy Iteration ◽  
Gradient Projection ◽  
Iteration Methods

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.

Truncated policy iteration methods

1984 ◽  
Vol 3 (5) ◽  
pp. 243-246 ◽  
Author(s):  
Ron S. Dembo ◽  
Moshe Haviv
Keyword(s):  
Policy Iteration ◽  
Iteration Methods

scholarly journals Parametric optimization of steel structures based on gradient projection method

2020 ◽  
pp. 192-220
Author(s):  
Vitalina Yurchenko ◽  
Ivan Peleshko
Keyword(s):  
Parametric Optimization ◽  
Optimization Problems ◽  
Steel Structure ◽  
Steel Structures ◽  
Gradient Projection ◽  
Truss Structures ◽  
Design System ◽  
Geometrical Parameters ◽  
Structural Members ◽  
Load Case

The main research goal is the development of a numerical methodology for solving parametric optimization problems of steel structures with orientation on software implementation in a computer-aided design system. The paper has proposed a new mathematical model for parametric optimization problems of steel structures. The design variable vector includes geometrical parameters of the structure (node coordinates), cross-sectional dimensions of the structural members, as well as initial pre-stressing forces introduced into the specified redundant members of the structure. The system of constraints covers load-carrying capacities constraints formulated for all design sections of structural members of the steel structure subjected to all ultimate load case combinations. The displacements constraints formulated for the specified nodes of the steel structure subjected to all serviceability load case combinations have been also included into the system of constraints. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used for solving the parametric optimization problem. A numerical algorithm for solving the formulated parametric optimization problems of steel structures has been developed in the paper. The comparison of the optimization results of truss structures presented by the paper confirms the validity of the optimum solutions obtained using the proposed numerical methodology.

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