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Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…

We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point. In contrast to the convex case, in the long history of this basic problem, the only known theoretical results on first-order…

We consider the large sum of DC (Difference of Convex) functions minimization problem which appear in several different areas, especially in stochastic optimization and machine learning. Two DCA (DC Algorithm) based algorithms are proposed:…

Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting…

Deep neural networks have gained tremendous popularity in last few years. They have been applied for the task of classification in almost every domain. Despite the success, deep networks can be incredibly slow to train for even moderate…

In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints. The algorithm solves a sequence of (separable) strongly convex problems and…

We propose a stochastic conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. Existing CGM variants for this template either suffer from slow convergence rates, or…

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…

Distributed optimization utilizes local computation and communication to realize a global aim of optimizing the sum of local objective functions. This article addresses a class of constrained distributed nonconvex optimization problems…

We propose a novel Learned Alternating Minimization Algorithm (LAMA) for dual-domain sparse-view CT image reconstruction. LAMA is naturally induced by a variational model for CT reconstruction with learnable nonsmooth nonconvex…

As a popular meta-learning approach, the model-agnostic meta-learning (MAML) algorithm has been widely used due to its simplicity and effectiveness. However, the convergence of the general multi-step MAML still remains unexplored. In this…

In the past few years, numerous deep learning methods have been proposed to address the task of segmenting salient objects from RGB images. However, these approaches depending on single modality fail to achieve the state-of-the-art…

Normalization techniques such as Batch Normalization have been applied successfully for training deep neural networks. Yet, despite its apparent empirical benefits, the reasons behind the success of Batch Normalization are mostly…

This paper presents an accelerated proximal gradient method for multiobjective optimization, in which each objective function is the sum of a continuously differentiable, convex function and a closed, proper, convex function. Extending…

Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…

Despite the recent development in machine learning, most learning systems are still under the concept of "black box", where the performance cannot be understood and derived. With the rise of safety and privacy concerns in public, designing…

Neural networks with ReLU activation function have been shown to be universal function approximators and learn function mapping as non-smooth functions. Recently, there is considerable interest in the use of neural networks in applications…

When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem…

This study introduces a novel technique for multi-view clustering known as the "Consensus Graph-Based Multi-View Clustering Method Using Low-Rank Non-Convex Norm" (CGMVC-NC). Multi-view clustering is a challenging task in machine learning…

This paper introduces a novel lightweight computational framework for enhancing images under low-light conditions, utilizing advanced machine learning and convolutional neural networks (CNNs). Traditional enhancement techniques often fail…