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This work presents a novel version of recently developed Gauss-Newton method for solving systems of nonlinear equations, based on upper bound of solution residual and quadratic regularization ideas. We obtained for such method global…
Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…
This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…
LP relaxation-based message passing algorithms provide an effective tool for MAP inference over Probabilistic Graphical Models. However, different LP relaxations often have different objective functions and variables of differing…
Optimization methods are essential in solving complex problems across various domains. In this research paper, we introduce a novel optimization method called Gaussian Crunching Search (GCS). Inspired by the behaviour of particles in a…
In solving hard computational problems, semidefinite program (SDP) relaxations often play an important role because they come with a guarantee of optimality. Here, we focus on a popular semidefinite relaxation of K-means clustering which…
This paper proposes a novel algorithm for signal classification problems. We consider a non-stationary random signal, where samples can be classified into several different classes, and samples in each class are identically independently…
When applying machine learning to problems in NLP, there are many choices to make about how to represent input texts. These choices can have a big effect on performance, but they are often uninteresting to researchers or practitioners who…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
Federated learning enables training on a massive number of edge devices. To improve flexibility and scalability, we propose a new asynchronous federated optimization algorithm. We prove that the proposed approach has near-linear convergence…
We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that…
We study the Kaczmarz methods for solving systems of quadratic equations, i.e., the generalized phase retrieval problem. The methods extend the Kaczmarz methods for solving systems of linear equations by integrating a phase selection…
Load balancing is the process of improving the Performance of a parallel and distributed system through is distribution of load among the processors [1-2]. Most of the previous work in load balancing and distributed decision making in…
Convex optimization is an essential tool for modern data analysis, as it provides a framework to formulate and solve many problems in machine learning and data mining. However, general convex optimization solvers do not scale well, and…
This paper presents a convex optimization-based solution to the design of state-feedback controllers for solving the linear quadratic regulator (LQR) problem of uncertain discrete-time systems with multiplicative noise. To synthesize a…
Algebraic multigrid (AMG) methods derive their optimal efficiency from the interplay between a relaxation process and a corresponding coarse grid correction. In many standard formulations, relaxation and coarse-graining are analyzed and…
We present novel minibatch stochastic optimization methods for empirical risk minimization problems, the methods efficiently leverage variance reduced first-order and sub-sampled higher-order information to accelerate the convergence speed.…
This paper studies the scheduling of a large population of non-preemptive flexible electric loads, each of which has a flexible starting time but once started will follow a fixed load shape until completion. We first formulate the…
Fair graph clustering is crucial for ensuring equitable representation and treatment of diverse communities in network analysis. Traditional methods often ignore disparities among social, economic, and demographic groups, perpetuating…
Finding relative pose between two calibrated images is a fundamental task in computer vision. Given five point correspondences, the classical five-point methods can be used to calculate the essential matrix efficiently. For the case of $N$…