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Optimization is a fundamental tool across science and engineering. This course aims to provide a comprehensive introduction to convex optimization. Topics include convex sets, functions, and optimization problems; optimality conditions; constrained optimization; widely used algorithms such as gradient methods, project gradient descent, Newton’s method, and proximal algorithms. Emphasis will be placed on both the theoretical underpinnings and practical implementation of convex optimization techniques in computational imaging and machine learning. This course will serve as the preliminary course for Modern Convex Optimization.