TU-A-BRB-01: Convex Optimization Techniques for Handling Delivery Time and Plan Complexity in Multi-Criteria VMAT Optimization

2011 ◽  
Vol 38 (6Part27) ◽  
pp. 3738-3738
Author(s):  
D Craft ◽  
T Bortfeld
Keyword(s):  
Convex Optimization ◽  
Optimization Techniques ◽  
Delivery Time

Balancing of Flexible Rotors Using Convex Optimization Techniques: Optimum Min-Max LMI Influence Coefficient Balancing

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Costin D. Untaroiu ◽  
Paul E. Allaire ◽  
William C. Foiles
Keyword(s):  
Convex Optimization ◽  
Optimization Theory ◽  
Numerical Algorithms ◽  
Optimization Methods ◽  
Industrial Applications ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Influence Coefficient ◽  
Flexible Rotors ◽  
Optimum Solution

In some industrial applications, influence coefficient balancing methods fail to find the optimum vibration reduction due to the limitations of the least-squares optimization methods. Previous min-max balancing methods have not included practical constraints often encountered in industrial balancing. In this paper, the influence coefficient balancing equations, with suitable constraints on the level of the residual vibrations and the magnitude of correction weights, are cast in linear matrix inequality (LMI) forms and solved with the numerical algorithms developed in convex optimization theory. The effectiveness and flexibility of the proposed method have been illustrated by solving two numerical balancing examples with complicated requirements. It is believed that the new methods developed in this work will help in reducing the time and cost of the original equipment manufacturer or field balancing procedures by finding an optimum solution of difficult balancing problems. The resulting method is called the optimum min-max LMI balancing method.

A CONVEX SUBMODEL WITH APPLICATION TO SYSTEM DESIGN

2004 ◽  
Vol 21 (01) ◽  
pp. 9-33
Author(s):  
JAVIER SALMERÓN ◽  
ÁNGEL MARÍN
Keyword(s):  
Convex Optimization ◽  
System Design ◽  
Optimality Conditions ◽  
Benders Decomposition ◽  
Optimal Solution ◽  
Lagrangean Relaxation ◽  
Optimization Techniques ◽  
Convex Model ◽  
Design Problems ◽  
Primal And Dual

In this paper, we present an algorithm to solve a particular convex model explicitly. The model may massively arise when, for example, Benders decomposition or Lagrangean relaxation-decomposition is applied to solve large design problems in facility location and capacity expansion. To attain the optimal solution of the model, we analyze its Karush–Kuhn–Tucker optimality conditions and develop a constructive algorithm that provides the optimal primal and dual solutions. This approach yields better performance than other convex optimization techniques.

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