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In this thesis we develop a novel framework to study smooth and strongly convex optimization algorithms, both deterministic and stochastic. Focusing on quadratic functions we are able to examine optimization algorithms as a recursive…

We propose a new family of subgradient- and gradient-based methods which converges with optimal complexity for convex optimization problems whose feasible region is simple enough. This includes cases where the objective function is…

We present a novel method for single image depth estimation using surface normal constraints. Existing depth estimation methods either suffer from the lack of geometric constraints, or are limited to the difficulty of reliably capturing…

Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…

This paper considers the analysis of continuous time gradient-based optimization algorithms through the lens of nonlinear contraction theory. It demonstrates that in the case of a time-invariant objective, most elementary results on…

We propose Adam-SHANG, a Lyapunov-guided Adam-type method that couples momentum, adaptive preconditioning, and a curvature-aware correction through a more stable lagged-preconditioner update. For stochastic smooth convex optimization, we…

Existing analysis of AdaGrad and other adaptive methods for smooth convex optimization is typically for functions with bounded domain diameter. In unconstrained problems, previous works guarantee an asymptotic convergence rate without an…

Consider composite nonconvex optimization problems where the objective function consists of a smooth nonconvex term (with Lipschitz-continuous gradient) and a convex (possibly nonsmooth) term. Existing parameter-free methods for such…

Gradient methods are among the simplest yet most widely used algorithms for unconstrained optimization. Motivated by a geometric property of the steepest descent (SD) method that can alleviate the zigzag behavior in quadratic problems, we…

The non-convexity of the artificial neural network (ANN) training landscape brings inherent optimization difficulties. While the traditional back-propagation stochastic gradient descent (SGD) algorithm and its variants are effective in…

This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…

We present a family of algorithms, called descent algorithms, for optimizing convex and non-convex functions. We also introduce a new first-order algorithm, called rescaled gradient descent (RGD), and show that RGD achieves a faster…

Parametric manifold optimization problems frequently arise in various machine learning tasks, where state functions are defined on infinite-dimensional manifolds. We propose a unified accelerated natural gradient descent (ANGD) framework to…

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of…

Monocular depth prediction plays a crucial role in understanding 3D scene geometry. Although recent methods have achieved impressive progress in terms of evaluation metrics such as the pixel-wise relative error, most methods neglect the…

In this paper, we develop new affine-invariant algorithms for solving composite convex minimization problems with bounded domain. We present a general framework of Contracting-Point methods, which solve at each iteration an auxiliary…

The essence of unsupervised anomaly detection is to learn the compact distribution of normal samples and detect outliers as anomalies in testing. Meanwhile, the anomalies in real-world are usually subtle and fine-grained in a…

Learning to reconstruct depths in a single image by watching unlabeled videos via deep convolutional network (DCN) is attracting significant attention in recent years. In this paper, we introduce a surface normal representation for…

In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current…

We propose a novel linesearch variant of the trust region normal map-based semismooth Newton method developed in [Ouyang and Milzarek, Math. Program. 212(1-2), 389--435 (2025)] for solving a class of nonsmooth, nonconvex composite-type…