×

Quasi-differentiable functions in non-differentiable optimization theory. (English) Zbl 0658.49008

Advances in mathematical optimization, Pap. Dedic. F. Nožička Occas. 70. Birthday, Math. Res. 45, 137-141 (1988).
[For the entire collection see Zbl 0649.00015.]
The concept of quasi-differentiable function is introduced. Relations between quasi-differentiability and Fréchet-differentiability are discussed. A modified steepest descent algorithm, which uses the quasi- differential is described. This algorithm enables us to solve one class of quasi-differentiable optimization problems considered in the further part of the paper. Another application to the solution of the so called continuous set covering problem is mentioned.
Reviewer: K.Zimmermann

MSC:

49J52 Nonsmooth analysis
26B05 Continuity and differentiation questions
90C30 Nonlinear programming
49J50 Fréchet and Gateaux differentiability in optimization

Citations:

Zbl 0649.00015