Multimodular functions and L-convex functions have been investigated almost independently, but they are, in fact, equivalent objects that can be related through a simple coordinate transformation. Some facts known for L-convex functions can be translated to new results for multimodular functions, and vice versa. In particular, the local optimality condition for global optimality found in the li...

Abstract: In this paper we study second order sufficient conditions for the strong-local optimality of singular Pontryagin extremals. In particular, we focus on the minimum-time problem for a control-affine system with vector inputs. We use Hamiltonian methods to prove that the coercivity of a suitably-defined second variation plus an involutivity assumption on the distribution of the controlle...

We investigate the general multi-armed bandit problem with multiple servers. We determine a condition on the reward processes su1⁄2cient to guarantee the optimality of the strategy that operates at each instant of time the projects with the highest Gittins indices. We call this strategy the Gittins index rule for multi-armed bandits with multiple plays, or brie ̄y the Gittins index rule. We show...

In this article we study a boundary control problem for an Oseen-type model of viscoelastic fluid flow. The existence of a unique optimal solution is proved and an optimality system is derived by the first-order necessary condition. We investigate finite element approximations to a solution of the optimality system, and a solution algorithm for the system based on the gradient method. © 2007 El...

This article deals with the problem of computing energy-minimal trajectories between the invariant manifolds in the neighborhood of the equilibrium point L1 of the restricted 3-body problem. Initializing a simple shooting method with solutions of the corresponding linear optimal control problem, we numerically compute energy-minimal extremals from the Pontryagin’s Maximum principle, whose optim...

Sparse principal component analysis (PCA) addresses the problem of finding a linear combination of the variables in a given data set 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 nece...