Minimization Problem

Minimization problems, central to numerous scientific fields, aim to find the input values that yield the lowest output of a given function. Current research focuses on developing efficient algorithms for various minimization contexts, including those involving multiple objectives, high-dimensional data (like in deep learning), and non-convex or non-smooth functions. These advancements leverage techniques such as gradient descent and its variants, alternating minimization, and stochastic methods, often tailored to specific problem structures (e.g., low-rank matrix completion). The resulting improvements in computational efficiency and solution accuracy have significant implications across diverse applications, from machine learning and image processing to natural language processing and even mathematical problem solving.