Related papers: Convex Quaternion Optimization for Signal Processi…
Quadratic assignment problem is one of the great challenges in combinatorial optimization. It has many applications in Operations research and Computer Science. In this paper, the author extends the most-used rounding approach to a…
In distributed detection, there does not exist an automatic way of generating optimal decision strategies for non-affine decision functions. Consequently, in a detection problem based on a non-affine decision function, establishing…
We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…
Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green and blue channels of color images. A low-rank approximation for a pure…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
Matrix completion (MC) is a promising technique which is able to recover an intact matrix with low-rank property from sub-sampled/incomplete data. Its application varies from computer vision, signal processing to wireless network, and…
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity…
Advances in numerical optimization have supported breakthroughs in several areas of signal processing. This paper focuses on the recent enhanced variants of the proximal gradient numerical optimization algorithm, which combine quasi-Newton…
Decentralized optimization is a common paradigm used in distributed signal processing and sensing as well as privacy-preserving and large-scale machine learning. It is assumed that several computational entities locally hold objective…
In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted…
Gradient methods have applications in multiple fields, including signal processing, image processing, and dynamic systems. In this paper, we present a nonlinear gradient method for solving convex supra-quadratic functions by developing the…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining…
Tensor recovery has recently arisen in a lot of application fields, such as transportation, medical imaging and remote sensing. Under the assumption that signals possess sparse and/or low-rank structures, many tensor recovery methods have…
Nonconvex optimization is central to modern machine learning, but the general framework of nonconvex optimization yields weak convergence guarantees that are too pessimistic compared to practice. On the other hand, while convexity enables…
Convex optimization problems arise naturally in quantum information theory, often in terms of minimizing a convex function over a convex subset of the space of hermitian matrices. In most cases, finding exact solutions to these problems is…
We propose a communication- and computation-efficient distributed optimization algorithm using second-order information for solving ERM problems with a nonsmooth regularization term. Current second-order and quasi-Newton methods for this…
Graph Neural Networks (GNNs) are key tools for graph representation learning, demonstrating strong results across diverse prediction tasks. In this paper, we present Convexified Message-Passing Graph Neural Networks (CGNNs), a novel and…
In communication networks, optimization is essential in enhancing performance metrics, e.g., network utility. These optimization problems often involve sum-of-products (or ratios) terms, which are typically non-convex and NP-hard, posing…
Tensor networks represent the state-of-the-art in computational methods across many disciplines, including the classical simulation of quantum many-body systems and quantum circuits. Several applications of current interest give rise to…