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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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Journal ArticleDOI
TL;DR: This paper uses a charging selection concept for plug-in electric vehicles (PEVs) to maximize user convenience levels while meeting predefined circuit-level demand limits, and develops a distributed optimization algorithm to solve the PEV-charging selection problem in a decentralized manner.
Abstract: This paper uses a charging selection concept for plug-in electric vehicles (PEVs) to maximize user convenience levels while meeting predefined circuit-level demand limits. The optimal PEV-charging selection problem requires an exhaustive search for all possible combinations of PEVs in a power system, which cannot be solved for the practical number of PEVs. Inspired by the efficiency of the convex relaxation optimization tool in finding close-to-optimal results in huge search spaces, this paper proposes the application of the convex relaxation optimization method to solve the PEV-charging selection problem. Compared with the results of the uncontrolled case, the simulated results indicate that the proposed PEV-charging selection algorithm only slightly reduces user convenience levels, but significantly mitigates the impact of the PEV-charging on the power system. We also develop a distributed optimization algorithm to solve the PEV-charging selection problem in a decentralized manner, i.e., the binary charging decisions (charged or not charged) are made locally by each vehicle. Using the proposed distributed optimization algorithm, each vehicle is only required to report its power demand rather than report several of its private user state information, mitigating the security problems inherent in such problem. The proposed decentralized algorithm only requires low-speed communication capability, making it suitable for real-time implementation.

219 citations

Journal ArticleDOI
TL;DR: A method is developed for the estimation of the essential matrix, giving the first guaranteed optimal algorithm for estimating the relative pose using a cost function based on reprojection errors.
Abstract: This paper introduces a new algorithmic technique for solving certain problems in geometric computer vision. The main novelty of the method is a branch-and-bound search over rotation space, which is used in this paper to determine camera orientation. By searching over all possible rotations, problems can be reduced to known fixed-rotation problems for which optimal solutions have been previously given. In particular, a method is developed for the estimation of the essential matrix, giving the first guaranteed optimal algorithm for estimating the relative pose using a cost function based on reprojection errors. Recently convex optimization techniques have been shown to provide optimal solutions to many of the common problems in structure from motion. However, they do not apply to problems involving rotations. The search method described in this paper allows such problems to be solved optimally. Apart from the essential matrix, the algorithm is applied to the camera pose problem, providing an optimal algorithm. The approach has been implemented and tested on a number of both synthetically generated and real data sets with good performance.

219 citations

Journal ArticleDOI
TL;DR: By defining a more general type of Lyapunov functionals, some new less conservative delay-dependent stability criteria are obtained and shown in terms of linear matrix inequalities (LMIs).
Abstract: In this paper, a novel method is developed for the stability problem of a class of neural networks with time-varying delay. New delay-dependent stability criteria in terms of linear matrix inequalities for recurrent neural networks with time-varying delay are derived by the newly proposed augmented simple Lyapunov-Krasovski functional. Different from previous results by using the first-order convex combination property, our derivation applies the idea of second-order convex combination and the property of quadratic convex function which is given in the form of a lemma without resorting to Jensen's inequality. A numerical example is provided to verify the effectiveness and superiority of the presented results.

219 citations

Proceedings ArticleDOI
28 Jun 2009
TL;DR: An adaptive line search scheme which allows to tune the step size adaptively and meanwhile guarantees the optimal convergence rate is proposed, which demonstrates the efficiency of the proposed Lassplore algorithm for large-scale problems.
Abstract: Logistic Regression is a well-known classification method that has been used widely in many applications of data mining, machine learning, computer vision, and bioinformatics. Sparse logistic regression embeds feature selection in the classification framework using the l1-norm regularization, and is attractive in many applications involving high-dimensional data. In this paper, we propose Lassplore for solving large-scale sparse logistic regression. Specifically, we formulate the problem as the l1-ball constrained smooth convex optimization, and propose to solve the problem using the Nesterov's method, an optimal first-order black-box method for smooth convex optimization. One of the critical issues in the use of the Nesterov's method is the estimation of the step size at each of the optimization iterations. Previous approaches either applies the constant step size which assumes that the Lipschitz gradient is known in advance, or requires a sequence of decreasing step size which leads to slow convergence in practice. In this paper, we propose an adaptive line search scheme which allows to tune the step size adaptively and meanwhile guarantees the optimal convergence rate. Empirical comparisons with several state-of-the-art algorithms demonstrate the efficiency of the proposed Lassplore algorithm for large-scale problems.

219 citations

Journal ArticleDOI
TL;DR: This article provides an alternative averaged mapping approach to the GPA, and provides two modifications of GPA so that strong convergence is guaranteed in infinite-dimensional Hilbert spaces.
Abstract: It is well known that the gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. In this article, we first provide an alternative averaged mapping approach to the GPA. This approach is operator-oriented in nature. Since, in general, in infinite-dimensional Hilbert spaces, GPA has only weak convergence, we provide two modifications of GPA so that strong convergence is guaranteed. Regularization is also applied to find the minimum-norm solution of the minimization problem under investigation.

219 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023392
2022849
20211,461
20201,673
20191,677
20181,580