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Stochastic optimization is playing an increasingly important in machine learning in the big data era. In this paper, we use forward-backward splitting for the stochastic optimization problems, where the objective is the sum of two functions: one is the expected risk function, another is a regularized term. At each iteration of this method, we just use a single sample to adjust the variables. We prove...
Quaternion-valued adaptive filters based on the mean square error (MSE) criterion have been extensively studied in recent years. However, the MSE cost function has only one degree of freedom, and to circumvent this problem, we propose another criterion which enables separate control of the magnitude and phase. Next, a quaternion least mean magnitude phase (QLMMP) filtering algorithm is introduced...
In this paper, minimum MSE based interference alignment (IA) algorithm is developed for the interfering broadcast channel (IBC), which models the multi-cell downlink system, underlying cognitive radio, device-to-device and other scenarios. The IA precoders and decoders are computed to minimize the MSE. Cascade design is used for IA precoder design, where the first component precoder is obtained by...
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes and analyzes a new Matrix Splitting Method (MSM) for minimizing composite functions. It can be viewed as a generalization of the classical Gauss-Seidel method...
We propose a novel parallel essentially cyclic asynchronous algorithm for the minimization of the sum of a smooth (nonconvex) function and a convex (nonsmooth) regularizer. The framework hinges on Successive Convex Approximation (SCA) techniques and on a new global model that describes many asynchronous environments in a more faithful and exhaustive way with respect to state-of-the-art models. A key...
We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of recovering a matrix X ∈ ℝd1 × d2 of rank r ≪ min(d1, d2) from incomplete linear observations, solving a sequence of quadratic problems. The easily implementable algorithm, which we call Harmonic Mean Iteratively Reweighted Least Squares (HM-IRLS), is superior compared to state-of-the-art algorithms for the low-rank...
In this paper, a fully distributed strategy is proposed to solve the N-coalition multi-agent games. The agents in the considered N-coalition multi-agent games are supposed to have limited access to the other players' actions. Consensus protocols, including a leader-following consensus protocol and a dynamic average consensus protocol, are leveraged to search for the Nash equilibrium of the N-coalition...
Distributed algorithms are proposed to solve distributed optimization problems for a network of strongly connected agents in this paper. The proposed algorithms are based on a combination of a leader-following consensus protocol and the gradient descent method/primal-dual dynamics. In the leader-following consensus protocol, each agent acts as a virtual leader that provides its local measurements...
Integration of the distributed energy resources in power distribution network has emerged as a significant method to optimize the operation and planning of the power distribution network. The optimal distributed generation placement comprises of obtaining the optimal size and location of the DGs to be placed. Various methods and techniques have been used to obtain the best possible results for optimal...
Motivated by applications in adaptive control, this article compares two recursive estimation algorithms for sparse estimation of linear dynamical (ARX) models. In most practical situations an accurate mathematical model estimation of a real system using the least number of parameters is highly desirable. The expectation of sparsity is imposed through minimization of an objective function that includes...
In this paper, we consider an unconstrained collaborative optimization of a sum of convex functions where agents make decisions using local information in the presence of random communication topologies. We recast the problem as a minimization of the sum of convex functions over a constraint set defined as the set of fixed value points of a random operator derived from weighted matrix of a random...
In the sparse Photoacoustic Microscopy system, a uniform random sampling scheme and low-rank matrix approximation-GoDec algorithm have been proposed for fast data acquisition and image recovery. However, this low-rank approximation algorithm leads to low resolution and fuzzy structure details. In this paper, the weighted Singular Value Thresholding algorithm is first applied in sparse PAM system to...
Group sparse representation (GSR) has shown great potential in image Compressive Sensing (CS) recovery, which can be considered as a low rank matrix approximation problem. The nuclear norm minimization can only minimize all the singular values simultaneously. Recent advances have suggested the truncated nuclear norm minimization (TNNM) to better approximate the matrix rank. In this paper, we connect...
This paper examines the nonconvex quadratically constrained quadratic programming (QCQP) problems using a decomposition method. It is well known that a QCQP can be transformed into a rank-one constrained optimization problem. Finding a rank-one matrix is computationally complicated, especially for large scale QCQPs. A decomposition method is applied to decompose the single rank-one constraint on original...
In this paper, we formulate the distributed optimization of multi-building energy systems as a cost minimization problem with spatially and temporally coupled constraints. The problem is divided into subproblems of each building at each time slot via Lagrangian dual decomposition. The strong duality of the primal and dual problem is proved, and distributed algorithms are proposed based on the subgradient...
We present a new method for cell segmentation which combines a marked point process model with a combinatorics-based method of finding global optima. The method employs an energy term that assesses possible segmentations by their fidelity to both local image information and a simple model of cell interaction, and we use a randomized iterative reweighting technique for its minimization. Our approach...
A new method for designing single/multiple unimodular waveforms with good weighted correlation properties, which is based on minimizing the weighted integrated sidelobe levels of waveforms, is developed. The main contributions of the paper lie in formulating the objective as a quartic form where Hadamard product of matrices is involved, converting the non-convex quartic optimization problem into a...
We study the problem of approximating a partially observed matrix by a product of two low-rank matrices where the data as well as the factors are constrained to be binary. This computationally challenging task is motivated by the single individual haplotyping problem which attracted considerable attention in computational biology and is of critical importance for personalized medicine applications...
Dictionary learning follows a synthesis framework; the dictionary is learnt such that the data can be synthesized / re-generated from the coefficients. Transform learning on the other hand is based on analysis formulation; it learns a transform so as to generate the coefficients. The basic formulations of dictionary learning and transform learning employ a Euclidean cost function for the data fidelity...
We propose a novel parallel asynchronous algorithmic framework for the minimization of the sum of a smooth (nonconvex) function and a convex (nonsmooth) regularizer. The framework hinges on Successive Convex Approximation (SCA) techniques and on a novel probabilistic model which describes in a unified way a variety of asynchronous settings in a more faithful and exhaustive way with respect to state-of-the-art...
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