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The minimum sum-of-squares clustering problem (MSSC), also known as $k$-means clustering, refers to the problem of partitioning $n$ data points into $k$ clusters, with the objective of minimizing the total sum of squared Euclidean distances…
The subgradient extragradient method for solving the variational inequality (VI) problem, which is introduced by Censor et al. \cite{CGR}, replaces the second projection onto the feasible set of the VI, in the extragradient method, with a…
There has been a surge of interest in learning optimal decision trees using mixed-integer programs (MIP) in recent years, as heuristic-based methods do not guarantee optimality and find it challenging to incorporate constraints that are…
Many kernel methods suffer from high time and space complexities and are thus prohibitive in big-data applications. To tackle the computational challenge, the Nystr\"om method has been extensively used to reduce time and space complexities…
Transformer-based generative models have achieved remarkable success across domains with various scaling law manifestations. However, our extensive experiments reveal persistent challenges when applying Transformer to recommendation…
Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed…
Generative models, such as the method of normalizing flows, have been suggested as alternatives to the standard algorithms for generating lattice gauge field configurations. Studies with the method of normalizing flows demonstrate the proof…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
In this work, we present and analyze C-SAGA, a (deterministic) cyclic variant of SAGA. C-SAGA is an incremental gradient method that minimizes a sum of differentiable convex functions by cyclically accessing their gradients. Even though the…
The wide applications of Generative adversarial networks benefit from the successful training methods, guaranteeing that an object function converges to the local minima. Nevertheless, designing an efficient and competitive training method…
A convolutional neural network (CNN) is useful for overcoming the trade-off between generation speed and accuracy in the process of synthesizing computer-generated holograms (CGHs). However, methods using a CNN have limited applicability as…
The branch-and-cut algorithm is the method of choice to solve large scale integer programming problems in practice. A key ingredient of branch-and-cut is the use of cutting planes which are derived constraints that reduce the search space…
This paper proposes a novel column generation framework for combinatorial software testing. In particular, it combines Mathematical Programming and Constraint Programming in a hybrid decomposition to generate covering arrays. The approach…
The motivation of this work is to improve the performance of standard stacking approaches or ensembles, which are composed of simple, heterogeneous base models, through the integration of the generation and selection stages for regression…
With the integration of large-scale renewable energy sources to power systems, many optimization methods have been applied to solve the stochastic/uncertain transmission-constrained unit commitment (TCUC) problem. Among all methods,…
Efficient transport algorithms are essential to the numerical resolution of incompressible fluid flow problems. Semi-Lagrangian methods are widely used in grid based methods to achieve this aim. The accuracy of the interpolation strategy…
When fitting statistical models, some predictors are often found to be correlated with each other, and functioning together. Many group variable selection methods are developed to select the groups of predictors that are closely related to…
In this paper, we present a structured solver based on the preconditioned conjugate gradient method (PCGM) for solving the linear quadratic (LQ) optimal control problem for $K \times N$ sub-systems connected in a two-dimensional (2D) grid…
Optimization via simulation has been well established to find optimal solutions and designs in complex systems. However, it still faces modeling and computational challenges when extended to the multi-stage setting. This survey reviews the…
A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…