# Multi-directional search: A direct search algorithm for parallel machines

## Abstract

In recent years there has been a great deal in the development of optimization algorithms which exploit the computational power of parallel computer architectures. The author has developed a new direct search algorithm, which he calls multi-directional search, that is ideally suited for parallel computation. His algorithm belongs to the class of direct search methods, a class of optimization algorithms which neither compute nor approximate any derivatives of the objective function. His work, in fact, was inspired by the simplex method of Spendley, Hext, and Himsworth, and the simplex method of Nelder and Mead. The multi-directional search algorithm is inherently parallel. The basic idea of the algorithm is to perform concurrent searches in multiple directions. These searches are free of any interdependencies, so the information required can be computed in parallel. A central result of his work is the convergence analysis for his algorithm. By requiring only that the function be continuously differentiable over a bounded level set, he can prove that a subsequence of the points generated by the multi-directional search algorithm converges to a stationary point of the objective function. This is of great interest since he knows of few convergence results for practical direct search algorithms. Hemore »

- Authors:

- Publication Date:

- Research Org.:
- Rice Univ., Houston, TX (USA)

- OSTI Identifier:
- 5827867

- Resource Type:
- Miscellaneous

- Resource Relation:
- Other Information: Thesis (Ph.D)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; PARALLEL PROCESSING; ALGORITHMS; PROGRAMMING; ARRAY PROCESSORS; MULTIPLICITY; OPTIMIZATION; SYNCHRONIZATION; TASK SCHEDULING; DATA PROCESSING; MATHEMATICAL LOGIC; PROCESSING; 990200* - Mathematics & Computers

### Citation Formats

```
Torczon, V J.
```*Multi-directional search: A direct search algorithm for parallel machines*. United States: N. p., 1989.
Web.

```
Torczon, V J.
```*Multi-directional search: A direct search algorithm for parallel machines*. United States.

```
Torczon, V J. Sun .
"Multi-directional search: A direct search algorithm for parallel machines". United States.
```

```
@article{osti_5827867,
```

title = {Multi-directional search: A direct search algorithm for parallel machines},

author = {Torczon, V J},

abstractNote = {In recent years there has been a great deal in the development of optimization algorithms which exploit the computational power of parallel computer architectures. The author has developed a new direct search algorithm, which he calls multi-directional search, that is ideally suited for parallel computation. His algorithm belongs to the class of direct search methods, a class of optimization algorithms which neither compute nor approximate any derivatives of the objective function. His work, in fact, was inspired by the simplex method of Spendley, Hext, and Himsworth, and the simplex method of Nelder and Mead. The multi-directional search algorithm is inherently parallel. The basic idea of the algorithm is to perform concurrent searches in multiple directions. These searches are free of any interdependencies, so the information required can be computed in parallel. A central result of his work is the convergence analysis for his algorithm. By requiring only that the function be continuously differentiable over a bounded level set, he can prove that a subsequence of the points generated by the multi-directional search algorithm converges to a stationary point of the objective function. This is of great interest since he knows of few convergence results for practical direct search algorithms. He also presents numerical results indicating that the multidirectional search algorithm is robust, even in the presence of noise. His results include comparisons with the Nelder-Mead simplex algorithm, the method of steepest descent, and a quasi-Newton method. One surprising conclusion of his numerical tests is that the Nelder-Mead simplex algorithm is not robust. He closes with some comments about future directions of research.},

doi = {},

url = {https://www.osti.gov/biblio/5827867},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1989},

month = {1}

}