The Minimization of Semicontinuous Functions: Mollifier Subgradients
- 1 January 1995
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 33 (1) , 149-167
- https://doi.org/10.1137/s0363012992238369
Abstract
To minimize discontinuous functions that arise in the context of systems with jumps, for example, we propose a new approach based on approximation via averaged functions (obtained by convolution with mollifiers). The properties of averaged functions are studied, after it is shown that they can be used in an approximation scheme consistent with minimization. A new notion of subgradient is introduced based on approximations generated by mollifiers and is exploited in the design of minimization proceduresKeywords
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