**CONVEX EXTENSION OF
DISCRETE-CONVEX FUNCTIONS AND APPLICATIONS IN OPTIMIZATION THE STRUCTURE OF
PARALLEL AND DISTRIBUTED PROCESSING SYSTEMS **

Tiit Riismaa

**Abstract**

A
method of description and optimization of the structure of multi-level parallel
and distributed processing systems is presented. The set of feasible structures
for such class of systems is defined. The representation of this set is
constructed in terms of the graph theory. A recursive algorithm is constructed
to solve the general problem of optimal multi-level paralleling procedure. For
the reduced statement two types of variable parameters are defined: for the
level size and for the relations of adjacent levels. Two different classes of
iteration methods are developed. For solving the reduced problem the recursive
algorithm is constructed, where index of level is the index of recursion. Also
a numerical method of local searching is developed. On each step of the
iteration the calculation of the value of objective function is required only
on some vertices of some kind of unit cube. Modelling
and optimization of the structure of multi-level processing system illustrate
the considered approach.

Lecture
Notes in Management Science (2011) Vol. 3: 75-90

3rd
International Conference on Applied Operational Research, Proceedings

©
Tadbir Operational Research Group Ltd. All rights reserved.

www.tadbir.ca

ISSN
2008-0050 (Print)

ISSN
1927-0097 (Online)

**ARTICLE OUTLINE**

·
**Introduction **

·
**Feasible Set Of
Multi-Level Parallel And Distributed Processing System **

·
**The Problem Of Optimal
Multi-Level Parallel And Distributed Processing System **

·
**Recursive Algorithm
For Solving The General Problem Of Optimal Multi-Level Parallel And Distributed
Processing System **

·
**Reduced Problem Of
Optimal Parallel And Distributed Processing System **

·
**Recursive Algorithm
For Solving The Reduced Problem Of Optimal Parallel And Distributed Processing
System **

·
**Mathematical
Properties Of The Reduced Problem Of Optimal Parallel And Distributed
Processing System **

·
**Algorithm Of Local
Searching For The Reduced Problem Of Optimal Multi-Level Parallel And
Distributed Processing System **

·
**Academic Example:
Optimization The Structure Of Multi-Level Parallel And Distributed Processing
System **

·
**Conclusion **

·
**References **