The present work develops a new approach for studying the dynamic evolution of a vector optimization problem. We introduce a convenient differential inclusion that rules the dynamics of the optimization problem. Actually we consider a sort of 'gradient system' defined by vector valued functions. The main tool used is a completely new adaptation to the vector problem of the notion of pseudogradient, which is a well-known concept in the modern critical point theory. Finally we study a special class of solutions of the above quoted differential inclusion: the slow solutions.
Miglierina, E., Slow solutions of differential inclusions and vector optimization, <<SET-VALUED ANALYSIS>>, 2004; 12 (3): 345-356. [doi:10.1023/B:SVAN.0000031332.10564.f0] [http://hdl.handle.net/10807/1829]
Slow solutions of differential inclusions and vector optimization
Miglierina, Enrico
2004
Abstract
The present work develops a new approach for studying the dynamic evolution of a vector optimization problem. We introduce a convenient differential inclusion that rules the dynamics of the optimization problem. Actually we consider a sort of 'gradient system' defined by vector valued functions. The main tool used is a completely new adaptation to the vector problem of the notion of pseudogradient, which is a well-known concept in the modern critical point theory. Finally we study a special class of solutions of the above quoted differential inclusion: the slow solutions.
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