Generalized convexity and global optimization
Monotone compositions (sums, products) of generalized convex functions are studied. Criteria of generalized convexity (quasiconvexity, pseudoconvexity) for various classes of differentiable functions are established. The special attention is given to various classes of fractional and homogeneous functions. An iterative algorithm for solving special classes of multi-extremal problems - global optimization of monotone compositions of generalized convex functions - is suggested. This algorithm realizes some ideas of branch and bound method and consists in successive correcting the bounds on the optimal value of the objective function. The concept of transition from {open_quotes}Variable space{close_quotes} to {open_quotes}image space{close_quotes} and investigation Pareto-boundary for corresponding multiple criteria problems is found very fruitful. The optimization of monotone compositions of linear (linear fractional) functions is considered separately. In this case the effective application of the linear programming technique is possible. The applicability of the algorithm to optimizing more complicated classes of functions is discussed.
- OSTI ID:
- 35872
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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