Related papers: Global optimality conditions for sensor placement,…
The localization problem in a wireless sensor network is to determine the coordination of sensor nodes using the known positions of some nodes (called anchors) and corresponding noisy distance measurements. There is a variety of different…
In this article we propose a new approach to an analysis of DC optimization problems. This approach was largely inspired by codifferential calculus and the method of codifferential descent and is based on the use of a so-called affine…
In this paper we extend a recent idea of formulating and regularizing inverse problems as minimization problems, so without using a forward operator, thus avoiding explicit evaluation of a parameter-to-state map. We do so by rephrasing…
In this work, we address the problem of optimally placing a finite number of sensors within a given region so as to minimize the mean or maximal distance to the points of the domain. To tackle this natural geometric performance criterion,…
This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…
Image segmentation is an inherently ill-posed problem and thus requires regularization in order to limit the search space to reasonable solutions. A majority of segmentation methods integrates these regularization terms in one way or the…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
This paper presents an adaptive numerical framework for solving exterior "sound-soft" scattering problems governed by the Helmholtz equation. By interpreting the Method of Fundamental Solutions through the lens of rational approximation, we…
Many machine learning tasks, such as learning with invariance and policy evaluation in reinforcement learning, can be characterized as problems of learning from conditional distributions. In such problems, each sample $x$ itself is…
Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world…
Optical wireless communication is a promising technology for underwater broadband access networks, which are particularly important for high-resolution environmental monitoring applications. This paper focuses on a deep sea monitoring…
Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive, and sometimes even impossible to…
We propose online algorithms for sequential learning in the contextual multi-armed bandit setting. Our approach is to partition the context space and then optimally combine all of the possible mappings between the partition regions and the…
We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…
Many specific problems ranging from theoretical probability to applications in statistical physics, combinatorial optimization and communications can be formulated as an optimal tuning of local parameters in large systems of interacting…
This paper primarily focuses on figuring out the best array of cameras, or visual sensors, so that such a placement enables the maximum utilization of these visual sensors. Maximizing the utilization of these cameras can convert to another…
Hu et. al 2018 studied a stochastic optimal control problem for fully coupled forward-backward stochastic control systems with a nonempty control domain. By assuming a weakly coupled condition, they established an approach to obtain the…
In recent times, various distributed optimization algorithms have been proposed for whose specific agent dynamics global optimality and convergence is proven. However, there exist no general conditions for the design of such algorithms. In…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
This paper investigates the optimality conditions for characterizing the local minimizers of the constrained optimization problems involving an $\ell_p$ norm ($0<p<1$) of the variables, which may appear in either the objective or the…