We provide sufficient optimality conditions for optimal control problems with bang-bang controls. Building on a structural assumption on the adjoint state, we additionally need a weak second-order condition. This second-order condition is formulated with functions from an extended critical cone, and it is equivalent to a formulation posed on measures supported on the set where the adjoint state...

Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given dataset with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to interpret the principal components and is applicable in a wide variety of fields including genetics and finance, just to name a few. We suggest a necessary co...

We develop a new notion of second-order complementarity with respect to the tangent subspace related to second-order necessary optimality conditions by the introduction of so-called tangent multipliers. We prove that around a local minimizer, a second-order stationarity residual can be driven to zero while controlling the growth of Lagrange multipliers and tangent multipliers, which gives a new...

This note is focused on a bounded control problem with boundary conditions. The control domain need not be convex. First-order necessary condition for optimality is obtained in the customary form of the maximum principle, and second-order necessary condition for optimality of singular controls is derived on the basis of second-order increment formula using the method of increments along with li...

Engineering of distributed computing systems requires understanding of principles of complex systems, which have not been yet identified. To address the situation we use a concept of structural complexity and present results of computational experiments suggesting the possibility of a general optimality condition of complex systems. The optimality condition introduces the structural complexity ...