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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Papers
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TL;DR: In this paper, the global asymptotic stability analysis problem for a class of uncertain stochastic Hopfield neural networks with discrete and distributed time-delays was studied.
223 citations
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TL;DR: The first attempt to characterize the uncertainties entering into the inner coupling matrix is made with the aid of the interval matrix approach, and a novel measurement model is proposed to account for these phenomena occurring with individual probability.
Abstract: In this paper, the H∞ state estimation problem is investigated for a class of complex networks with uncertain coupling strength and incomplete measurements. With the aid of the interval matrix approach, we make the first attempt to characterize the uncertainties entering into the inner coupling matrix. The incomplete measurements under consideration include sensor saturations, quantization, and missing measurements, all of which are assumed to occur randomly. By introducing a stochastic Kronecker delta function, these incomplete measurements are described in a unified way and a novel measurement model is proposed to account for these phenomena occurring with individual probability. With the measurement model, a set of H∞ state estimators is designed such that, for all admissible incomplete measurements as well as the uncertain coupling strength, the estimation error dynamics is exponentially mean-square stable and the H∞ performance requirement is satisfied. The characterization of the desired estimator gains is derived in terms of the solution to a convex optimization problem that can be easily solved using the semidefinite program method. Finally, a numerical simulation example is provided to demonstrate the effectiveness and applicability of the proposed design approach.
222 citations
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TL;DR: This paper analyzes the convergence rate of the alternating minimization method and establishes a nonasymptotic sublinear rate of convergence where the multiplicative constant depends on the minimal block Lipschitz constant, and studies the convergence properties of a decomposition-based approach designed to solve convex problems involving sums of norms.
Abstract: This paper is concerned with the alternating minimization (AM) method for solving convex minimization problems where the decision variables vector is split into two blocks. The objective function is a sum of a differentiable convex function and a separable (possibly) nonsmooth extended real-valued convex function, and consequently constraints can be incorporated. We analyze the convergence rate of the method and establish a nonasymptotic sublinear rate of convergence where the multiplicative constant depends on the minimal block Lipschitz constant. We then analyze the iteratively reweighted least squares (IRLS) method for solving convex problems involving sums of norms. Based on the results derived for the AM method, we establish a nonasymptotic sublinear rate of convergence of the IRLS method. In addition, we show an asymptotic rate of convergence whose efficiency estimate does not depend on the data of the problem. Finally, we study the convergence properties of a decomposition-based approach designed t...
222 citations
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TL;DR: In this paper, the authors provide an overview of the state-of-the-art results on communication resource allocation over space, time, and frequency for emerging cognitive radio (CR) wireless networks.
Abstract: This article provides an overview of the state-of-art results on communication resource allocation over space, time, and frequency for emerging cognitive radio (CR) wireless networks. Focusing on the interference-power/interference-temperature (IT) constraint approach for CRs to protect primary radio transmissions, many new and challenging problems regarding the design of CR systems are formulated, and some of the corresponding solutions are shown to be obtainable by restructuring some classic results known for traditional (non-CR) wireless networks. It is demonstrated that convex optimization plays an essential role in solving these problems, in a both rigorous and efficient way. Promising research directions on interference management for CR and other related multiuser communication systems are discussed.
221 citations
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TL;DR: This work proposes a stochastic primal-dual coordinate method, which alternates between maximizing over one (or more) randomly chosen dual variable and minimizing over the primal variable, and develops an extension to non-smooth and nonstrongly convex loss functions.
Abstract: We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a stochastic primal-dual coordinate (SPDC) method, which alternates between maximizing over a randomly chosen dual variable and minimizing over the primal variables. An extrapolation step on the primal variables is performed to obtain accelerated convergence rate. We also develop a mini-batch version of the SPDC method which facilitates parallel computing, and an extension with weighted sampling probabilities on the dual variables, which has a better complexity than uniform sampling on unnormalized data. Both theoretically and empirically, we show that the SPDC method has comparable or better performance than several state-of-the-art optimization methods.
221 citations