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We study a generic principal-agent problem in continuous time on a finite time horizon. We introduce a framework in which the agent is allowed to employ measure-valued controls and characterise the continuation utility as a solution to a…
One of the oldest and most common structural engineering issues is the elastic buckling of circular rings under external pressure, which has a fundamental importance in a number of applications in general mechanics, engineering and…
We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results give strong error probability bounds that are "sub-Gaussian"~even when the randomness of the…
The consensus problem in distributed computing involves a network of agents aiming to compute the average of their initial vectors through local communication, represented by an undirected graph. This paper focuses on the studying of this…
We make several improvements on the results of M.-T. Wang in [8] and his joint paper with M.-P. Tsui [7] concerning the long time existence and convergence for solutions of mean curvature flow in higher co-dimension. Both the curvature…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
Implementation of controlled-rotations using entanglement is considered. We show that the successful probability is closely related to the entanglement and the rotation angle. The successful probability will increase if we increase the…
Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through…
We present a simple communication complexity problem where three parties benefit from sharing bound entanglement. This demonstrates that entanglement distillability of the shared state is not necessary in order to surpass classical…
The rules of canonical quantization normally offer good results, but sometimes they fail, e.g., leading to quantum triviality ($=$ free) for certain examples that are classically nontrivial ($\ne$ free). A new procedure, called Enhanced…
We make some remarks on a variant of the classical Tikhonov regularization in optimal control under PDEs which allows for a certain flexibility in dealing with non-linearities and state restrictions, in the sense that differential…
The nonexistence of "cusp solutions" of prescribed mean curvature boundary value problems in $\Omega\times{\bf R}$ when $\Omega$ is a domain in ${\bf R}^{2}$ is proven in certain cases and an application to radial limits at a corner is…
In this paper, we present an iterative three-point method with memory based on the family of King's methods to solve nonlinear equations. This proposed method has eighth order convergence and costs only four function evaluations per…
The Ring Loading Problem is an optimal routing problem arising in the planning of optical communication networks which use bidirectional SONET rings. In mathematical terms, it is an unsplittable multicommodity flow problem on undirected…
We determine the optimal entanglement rate of quantum state merging when assuming that the state is unknown except for its membership in a certain set of states. We find that merging is possible at the lowest rate allowed by the individual…
We present deviation bounds for self-normalized averages and applications to estimation with a random number of observations. The results rely on a peeling argument in exponential martingale techniques that represents an alternative to the…
Entanglement is known to boost the efficiency of classical communication. In distributed computation, for instance, exploiting entanglement can reduce the number of communicated bits or increase the probability to obtain a correct answer.…
We improve recently introduced consensus-based optimization method, proposed in [R. Pinnau, C. Totzeck, O. Tse and S. Martin, Math. Models Methods Appl. Sci., 27(01):183--204, 2017], which is a gradient-free optimization method for general…
We establish the first general regularity result for constrained optimal control problems arising naturally in mathematical physics and mathematical biology. Namely, we prove that for a large class of problems of the form ``maximise $\int…
If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present…