Primal and dual problems of optimal control with linear, quadratic or piecewise linear-quadratic convex objective are considered in which a linear dynamical system is subjected to linear inequality constraints that could jointly involve states and controls. It is shown that when such constraints, except for the ones on controls only, are represented by penalty terms, and a mild coercivity condi...

We present structural properties of the farthest line-segment Voronoi diagram in the piecewise linear L∞ and L1 metrics, which are computationally simpler than the standard Euclidean distance and very well suited for VLSI applications. We introduce the farthest line-segment hull, a closed polygonal curve that characterizes the regions of the farthest line-segment Voronoi diagram, and is related...

A generalized semitoric system F := (J,H) : M → R on a symplectic 4-manifold is an integrable system whose essential properties are that F is a proper map, its set of regular values is connected, J generates an S-action and is not necessarily proper. These systems can exhibit focusfocus singularities, which correspond to fibers of F which are topologically multi-pinched tori. The image F (M) is...

In this paper we extend the standard bundle proximal method for finding the minimum of a convex not necessarily differentiable function on the nonnegative orthant. The strategy consists in approximating the objective function by a piecewise linear convex function and using distance–like functions based on second order homogeneous kernels. First we prove the convergence of this new bundle interi...

Capacity control is a very important problem in civil infrastructure operation, but no general model exists for it. In this project we • Formulate the real-time capacity control problem of a single facility • Perform dynamic programming to search for the optimal solution • Implement piecewise linear regression to update the objective function, and SCP to update the policy • Extend the model to ...

ABSTRACT We introduce the class of piecewise convex transformations, and study their complexity. We apply the results to the complexity of polygonal billiards on surfaces of constant curvature.We introduce the class of piecewise convex transformations, and study their complexity. We apply the results to the complexity of polygonal billiards on surfaces of constant curvature.

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