Topic
Convex optimization
About: Convex optimization is a research topic. Over the lifetime, 24906 publications have been published within this topic receiving 908795 citations. The topic is also known as: convex optimisation.
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01 Sep 2009TL;DR: This paper revisits regularization and shows that appropriate adaptive regularization substantially improves the accuracy of estimated motion fields and systematically evaluates regularizes which adoptively favor rigid body motion (if supported by the image data) and motion field discontinuities that coincide with discontinUities of the image structure.
Abstract: The accurate estimation of motion in image sequences is of central importance to numerous computer vision applications. Most competitive algorithms compute flow fields by minimizing an energy made of a data and a regularity term. To date, the best performing methods rely on rather simple purely geometric regularizes favoring smooth motion. In this paper, we revisit regularization and show that appropriate adaptive regularization substantially improves the accuracy of estimated motion fields. In particular, we systematically evaluate regularizes which adoptively favor rigid body motion (if supported by the image data) and motion field discontinuities that coincide with discontinuities of the image structure. The proposed algorithm relies on sequential convex optimization, is real-time capable and outperforms all previously published algorithms by more than one average rank on the Middlebury optic flow benchmark.
217 citations
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TL;DR: In this article, three practical operating protocols for simultaneously transmitting and reflecting (STAR) reconfigurable intelligent surfaces (RISs) are investigated, where the incident wireless signal is divided into transmitted and reflected signals passing into both sides of the space surrounding the surface, thus facilitating a fullspace manipulation of signal propagation.
Abstract: The novel concept of simultaneously transmitting and reflecting (STAR) reconfigurable intelligent surfaces (RISs) is investigated, where the incident wireless signal is divided into transmitted and reflected signals passing into both sides of the space surrounding the surface, thus facilitating a full-space manipulation of signal propagation. Based on the introduced basic signal model of ‘STAR’, three practical operating protocols for STAR-RISs are proposed, namely energy splitting (ES), mode switching (MS), and time switching (TS). Moreover, a STAR-RIS aided downlink communication system is considered for both unicast and multicast transmission, where a multi-antenna base station (BS) sends information to two users, i.e., one on each side of the STAR-RIS. A power consumption minimization problem for the joint optimization of the active beamforming at the BS and the passive transmission and reflection beamforming at the STAR-RIS is formulated for each of the proposed operating protocols, subject to communication rate constraints of the users. For ES, the resulting highly-coupled non-convex optimization problem is solved by an iterative algorithm, which exploits the penalty method and successive convex approximation. Then, the proposed penalty-based iterative algorithm is extended to solve the mixed-integer non-convex optimization problem for MS. For TS, the optimization problem is decomposed into two subproblems, which can be consecutively solved using state-of-the-art algorithms and convex optimization techniques. Finally, our numerical results reveal that: 1) the TS and ES operating protocols are generally preferable for unicast and multicast transmission, respectively; and 2) the required power consumption for both scenarios is significantly reduced by employing the proposed STAR-RIS instead of conventional reflecting/transmiting-only RISs.
217 citations
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TL;DR: Three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations are proposed and it is shown that the proposed convex optimization based approaches are more accurate in predictive performance, faster, and more reliable in recovering a known multilinear structure than conventional approaches.
Abstract: In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations All approaches are formulated as convex minimization problems Therefore, the minimum is guaranteed to be unique The proposed approaches can automatically estimate the number of factors (rank) through the optimization Thus, there is no need to specify the rank beforehand The key technique we employ is the trace norm regularization, which is a popular approach for the estimation of low-rank matrices In addition, we propose a simple heuristic to improve the interpretability of the obtained factorization The advantages and disadvantages of three proposed approaches are demonstrated through numerical experiments on both synthetic and real world datasets We show that the proposed convex optimization based approaches are more accurate in predictive performance, faster, and more reliable in recovering a known multilinear structure than conventional approaches
217 citations
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TL;DR: A design methodology that combines average consensus algorithms and separation of time-scales ideas is proposed and this strategy is proved, under suitable hypotheses, to be globally convergent to the true minimizer.
Abstract: We address the problem of distributed unconstrained convex optimization under separability assumptions, i.e., the framework where each agent of a network is endowed with a local private multidimensional convex cost, is subject to communication constraints, and wants to collaborate to compute the minimizer of the sum of the local costs. We propose a design methodology that combines average consensus algorithms and separation of time-scales ideas. This strategy is proved, under suitable hypotheses, to be globally convergent to the true minimizer. Intuitively, the procedure lets the agents distributedly compute and sequentially update an approximated Newton-Raphson direction by means of suitable average consensus ratios. We show with numerical simulations that the speed of convergence of this strategy is comparable with alternative optimization strategies such as the Alternating Direction Method of Multipliers. Finally, we propose some alternative strategies which trade-off communication and computational requirements with convergence speed.
216 citations
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TL;DR: This paper considers transmit optimization in multi-input multi-output (MIMO) wiretap channels, wherein they aim at maximizing the secrecy capacity or rate of an MIMO channel overheard by one or multiple eavesdroppers, and proposes an alternating optimization (AO) approach to tackle these secrecy optimization problems.
Abstract: This paper considers transmit optimization in multi-input multi-output (MIMO) wiretap channels, wherein we aim at maximizing the secrecy capacity or rate of an MIMO channel overheard by one or multiple eavesdroppers. Such optimization problems are nonconvex, and appear to be difficult especially in the multi-eavesdropper scenario. In this paper, we propose an alternating optimization (AO) approach to tackle these secrecy optimization problems. We first consider the secrecy capacity maximization (SCM) problem in the single eavesdropper scenario. An AO algorithm is derived through a judicious SCM reformulation. The algorithm conducts some kind of reweighting and water-filling in an alternating fashion, and thus is computationally efficient to implement. We also prove that the AO algorithm is guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point of the SCM problem. Then, we turn our attention to the multiple eavesdropper scenario, where the artificial noise (AN)-aided secrecy rate maximization (SRM) problem is considered. Although the AN-aided SRM problem has a more complex problem structure than the previous SCM, we show that AO can be extended to deal with the former, wherein the problem is handled by solving convex problems in an alternating fashion. Again, the resulting AO method is proven to have KKT point convergence guarantee. For fast implementation, a custom-designed AO algorithm based on smoothing and projected gradient is also derived. The secrecy rate performance and computational efficiency of the proposed algorithms are demonstrated by simulations.
216 citations