2022/02/03 by A. V. Dmitruk, Dmitruk, A. V., Nikolai P. Osmolovskii +1
Computer Science · Mathematics · Engineering · #Optimization and Variational Analysis #Numerical methods in inverse problems #Aerospace Engineering and Control Systems
paper · pdf · doi:10.48550/arxiv.2202.01707
We consider the simplest optimal control problem with one nonregular mixed inequality constraint, i.e. when its gradient in the control can vanish on the zero surface. Using the Dubovitskii--Milyutin theorem on the approximate separation of convex cones, we prove a first or der necessary condition for a weak minimum in the form of the so-called local minimum principle, which is formulated in terms of functions of bounded variation, integrable functions, and Lebesgue--Stieltjes measures, and does not use functionals on the space of measurable bounded functions. Two illustrative examples are given. The work is based on results by Milyutin.