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One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
Modal decomposition techniques, such as Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Singular Spectrum Analysis (SSA), have advanced time-frequency signal analysis since the early 21st century. These methods…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…
This work is concerned with the prime factor decomposition (PFD) of strong product graphs. A new quasi-linear time algorithm for the PFD with respect to the strong product for arbitrary, finite, connected, undirected graphs is derived.…
Distributed optimization is fundamental to modern machine learning applications like federated learning, but existing methods often struggle with ill-conditioned problems and face stability-versus-speed tradeoffs. We introduce fractional…
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications in algebraic geometry and beyond. We have previously reported on an implementation of CAD in Maple which offers…
The Proportional-Integral-Derivative Controller is widely used in industries for process control applications. Fractional-order PID controllers are known to outperform their integer-order counterparts. In this paper, we propose a new…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
High\-cardinality categorical variables pose significant challenges in machine learning, particularly in terms of computational efficiency and model interpretability. Traditional one\-hot encoding often results in high\-dimensional sparse…
We show {\it semidefinite programming} (SDP) feasibility problem is equivalent to solving a {\it convex hull relaxation} (CHR) for a finite system of quadratic equations. On the one hand, this offers a simple description of SDP. On the…
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
We consider $N$-way data arrays and low-rank tensor factorizations where the time mode is coded as a sparse linear combination of temporal elements from an over-complete library. Our method, Shape Constrained Tensor Decomposition (SCTD) is…
In this paper, we address a long-standing challenge: how to achieve both efficiency and scalability in solving semidefinite programming problems. We propose breakthrough acceleration techniques for a wide range of low-rank…
This paper explores a new class of constrained difference programming problems, where the objective and constraints are formulated as differences of functions, without requiring their convexity. To investigate such problems, novel variants…
Hybrid Bayesian networks (HBN) contain complex conditional probabilistic distributions (CPD) specified as partitioned expressions over discrete and continuous variables. The size of these CPDs grows exponentially with the number of parent…