RT Journal Article
SR 00
ID 10.1137/S0363012992238369
A1 Ermoliev, Y.M.
A1 Norkin, V.I.
A1 Wets, R.J.-B.
T1 The minimization of semicontinuous functions: Mollifier subgradients
JF SIAM Journal on Control and Optimization
YR 1995
FD 1995
VO 33
IS 1
SP 149
OP 167
K1 impulse control; discrete events systems; averaged functions; subgradients; subdifferentiability; stochastic quasi-gradients; epi-convergence
AB 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 procedures.
PB Society for Industrial and Applied Mathematics (SIAM)
SN 1095-7138
LK https://pure.iiasa.ac.at/id/eprint/4252/