In this paper, we identify a fundamental algorithmic problem that we term space-constrained dynamic covering (SCDC), arising in many modern-day web applications, including ad-serving and online recommendation systems in eBay and Netflix. Roughly speaking, SCDC applies two restrictions to the well-studied Max-Coverage problem [9]: Given an integer k, X = {1, 2, . . . , n} and I = {S1, . . . , Sm...

We consider the problem of minimizing the distance ‖f − φ‖Lp(K), where K is a subset of the complex unit circle ∂D and φ ∈ C(K), subject to the constraint that f lies in the Hardy space H(D) and |f | ≤ g for some positive function g. This problem occurs in the context of filter design for causal LTI systems. We show that the optimization problem has a unique solution, which satisfies an extrema...

planning robot trajectory is a complex task that plays a significant role in design and application of robots in task space. the problem is formulated as a trajectory optimization problem which is fundamentally a constrained nonlinear optimization problem. open-loop optimal control method is proposed as an approach for trajectory optimization of cable parallel manipulator for a given two-end-po...

Abstract We show that the homogeneous and 2-lobe Delaunay tori in 3-sphere provide only isothermic constrained Willmore 3-space with energy below $$8\pi $$ 8 π . In particular, every torus non-rectangular conformal class is non-degenerated.