Related papers: Scintillation Minimization versus Intensity Maximi…
We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…
We consider an optimal control problem describing a laser-induced population transfer on a $n$-level quantum system. For a convex cost depending only on the moduli of controls (i.e. the lasers intensities), we prove that there always exists…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
We study an inverse problem for the wave equation where localized wave sources in random scattering media are to be determined from time resolved measurements of the waves at an array of receivers. The sources are far from the array, so the…
We numerically examine the spatial evolution of the structure of coherent and partially coherent laser beams, including the optical vortices, propagating in turbulent atmospheres. The influence of beam fragmentation and wandering relative…
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…
In this paper, we study the problem of reducing the energy consumption in a mobile communication network; we select the smallest set of active base stations that can preserve the quality of service (the minimum data rate) required by the…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
Detecting hidden convexity is one of the tools to address nonconvex minimization problems. After giving a formal definition of hidden convexity, we introduce the notion of conditional infimum, as it will prove instrumental in detecting…
In this paper, the multiple-input multiple-output (MIMO) transmit beampattern matching problem is considered. The problem is formulated to approximate a desired transmit beampattern (i.e., an energy distribution in space and frequency) and…
In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…
We present a theory for wave scintillation in the situation with a time-dependent partially coherent source and a time-dependent randomly heterogeneous medium. Our objective is to understand how the scintillation index of the measured…
An investigation on stochastic deflection of high-energy negatively charged particles in a bent crystal was carried out. On the basis of analytical calculation and numerical simulation it was shown that it exists a maximum angle at which…
A wireless packet network is considered in which each user transmits a stream of packets to its destination. The transmit power of each user interferes with the transmission of all other users. A convex cost function of the completion times…
Beam angle optimization (BAO) largely determines the performance of fixed-field intensity modulated radiation therapy (IMRT), and it is usually considered as non-convex optimization and an NP hard problem. In this work, BAO is reformulated…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
High light collection efficiency is an important requirement in any application of scintillation detectors. The purpose of this study is to investigate the possibility for improving this parameter in cryogenic scintillation bolometers,…
In radiation therapy, mathematical methods have been used for optimizing treatment planning for delivery of sufficient dose to the cancerous cells while keeping the dose to critical surrounding structures minimal. This optimization problem…
Measurements have been performed of scintillation light intensities emitted from various inorganic scintillators irradiated with low-energy beams of highly-charged ions from an electron beam ion source (EBIS) and an electron cyclotron…