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In the era of big data and artificial intelligence, optimization and machine learning have become indispensable pillars of technological innovation, reshaping industries from healthcare and finance to smart manufacturing and autonomous systems. Optimization provides the mathematical framework for solving complex decisionª²making problems, while machine learning enables systems to learn from data and adapt dynamically¡ªtheir synergy has unlocked unprecedented possibilities in both academic research and realª²world applications. This book is crafted to bridge the gap between theoretical rigor and practical utility, guiding readers to grasp the core logic of this interdisciplinary field.
This book adheres to three core principles: Solidify Foundations, Clarify Principles, and Emphasize Applications. First, it prioritizes fundamental knowledge. Instead of chasing fleeting academic trends, we focus on timeless concepts, algorithms, and models that form the backbone of optimization and machine learning. We balance classical theories with cuttingª²edge developments, ensuring content aligns with the latest disciplinary progress while remaining grounded in essentials. Second, it emphasizes conceptual clarity. We strive to explain not only ¡°what¡± each algorithm does but also ¡°why¡± it works. Complex mathematical derivations are simplified without sacrificing rigor, and intuitive examples are used to unpack abstract ideas. Our goal is to help readers build a deep, intuitive understanding rather than merely memorize formulas or steps. Third, it integrates theory with practice. We highlight how optimization algorithms drive machine learning model training (e.g., gradient descent for neural networks, convex optimization for support vector machines) and include case studies that demonstrate how to apply these tools to realª²world problems. This approach equips readers with both theoretical knowledge and problemª²solving skills.
The book is structured into 8 chapters. Chapter 1 provides a basic overview; Chapter 2 focuses on the content of optimization basics; Chapter 3 explains the unconstrained optimization problem; Chapter 4 introduces the constrained optimization problem; Chapter 5 elaborates on the optimization with neural networks; Chapter 6 systematically explores how neural networks are applied in sequence modeling and visual tasks, focusing on RNNs and Vision Transformers; Chapter 7 focuses on neural network methods under limitedª²data conditions, explaining how singleª²image and singleª²scene learning expand computer vision capabilities through internal structural modeling; Chapter 8 presents a unified optimizationª²oriented overview of generative models, introducing their principles and representative frameworks.
This book is primarily designed for undergraduates and postgraduates majoring in computer science, data science, electrical engineering, mathematics, and related fields. It assumes basic knowledge of calculus, linear algebra, probability, and statistics¡ªfoundational topics typically covered in early undergraduate coursework. Additionally, it serves as a valuable reference for researchers and engineers seeking to strengthen their theoretical foundation or explore new applications of optimization and machine learning.
