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In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the…
This paper optimizes the step coefficients of first-order methods for smooth convex minimization in terms of the worst-case convergence bound (i.e., efficiency) of the decrease in the gradient norm. This work is based on the performance…
The excitation of microresonators using focused intensity modulated light, known as photothermal excitation, is gaining significant attention due to its capacity to accurately excite microresonators without distortions, even in liquid…
A problem of vibration control of smart beams was addressed in various publications which primarily utilize collocated sensors and actuators and neglect the effect of measurement noise in the observer design. This paper develops a natural…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
We study the control of coherent light propagation through multiple-scattering media in the presence of measurement noise. In our experiments, we use a two-step optimization procedure to find the optimal incident wavefront. We conclude that…
We consider the problem of estimating the possibly non-convex cost of an agent by observing its interactions with a nonlinear, non-stationary and stochastic environment. For this inverse problem, we give a result that allows to estimate the…
This study proposes introducing convex optimization to find initial perturbations of atmospheric states to realize specified changes in subsequent weather. In the proposed method, we formulate and solve an inverse problem to find effective…
The globally optimal robust adaptive beamforming (RAB) solution is studied for worst-case signal-to-interference-plus-noise ratio (SINR) maximization (the maximin SINR problem) under convex and closed uncertainty sets for the desired signal…
Quantum-intensity-correlated twin beams of light can be used to measure absorption with precision beyond the classical shot-noise limit. The degree to which this can be achieved with a given estimator is defined by the quality of the…
A strict analytical solution of the problem of spin-noise signal formation in a volume medium with randomly moving spin carriers is presented. The treatment is performed in the model of light scattering in a medium with fluctuating…
Nonconvex functionals with spherical symmetry are studied. Existence of one and radial symmetry of all global minimizers is shown with an approach based on convex relaxation.
This paper presents a convex approach to the optimization of a cooperative rendezvous, that is, the problem of two distant spacecraft that simultaneously operate to get closer. Convex programming guarantees convergence towards the optimal…
The design of a set of beamformers for the multiuser multiple-input single-output (MISO) downlink that provides the receivers with prespecified levels of quality-of-service (QoS) can be quite challenging when the channel state information…
We numerically examine the spatial evolution of the structure of coherent and partially coherent laser beams (PCBs), including the optical vortices, propagating in turbulent atmospheres. The influence of beam fragmentation and wandering…
In this letter, we consider optimal hybrid beamforming design to minimize the transmission power under individual signal-to-interference-plus-noise ratio (SINR) constraints in a multiuser massive multiple-input-multiple-output (MIMO)…
Spatially splitting nonclassical light beams is in principle prohibited due to noise contamination during beam splitting. We propose a platform based on thermal motion of atoms to realize spatial multiplexing of squeezed light. Light…
In this paper, a downlink non-orthogonal multiple access (NOMA) network is studied. We investigate the problem of jointly optimizing user pairing and beamforming design to maximize the minimum rate among all users. The considered problem…
The Illumination Problem may be phrased as the problem of covering a convex body in Euclidean $n$-space by a minimum number of translates of its interior. By a probabilistic argument, we show that, arbitrarily close to the Euclidean ball,…
Convex relaxations of the optimal finger selection algorithm are proposed for a minimum mean square error (MMSE) Rake receiver in an impulse radio ultra-wideband system. First, the optimal finger selection problem is formulated as an…