Simplicial decomposition and dual methods for nonlinear networks
This study is concerned with the development of algorithms for minimizing a nonlinear objective function subject to linear constraints. Special attention is given to models that have network constraints with possible bounds on the variables because they have many applications in areas such as transportation science, engineering, and economics. The first approach studied is a restricted version of the simplicial decomposition algorithm. This method allows the user to treat the maximum size of the generated simplices as a parameter. When the parameter is at its minimum value, the method reduces to the Frank-Wolfe algorithm; when at its maximum, it is the original simplicial decomposition of von Hohenbalken and Holloway. The second approach is concerned with the application of conjugate gradient-based methods to solve dual formulations of problems where the objective function is separable, strictly convex, and quadratic. These methods exploit both the sparsity and structure of the constraint matrix. Conditions for finite and superlinear convergence of these techniques are also discussed, and computational results on a variety of large test problems are presented.
- Research Organization:
- Florida Univ., Gainesville (USA)
- OSTI ID:
- 5298907
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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