## EE 364A: Convex Optimization I (CME 364A)

Convex sets, functions, and optimization problems. The basics of convex analysis and theory of convex programming: optimality conditions, duality theory, theorems of alternative, and applications. Least-squares, linear and quadratic programs, semidefinite programming, and geometric programming. Numerical algorithms for smooth and equality constrained problems; interior-point methods for inequality constrained problems. Applications to signal processing, communications, control, analog and digital circuit design, computational geometry, statistics, machine learning, and mechanical engineering. Prerequisite: linear algebra such as
EE263, basic probability.

Terms: Win
| Units: 3

Instructors:
Ayazifar, B. (PI)
;
Boyd, S. (PI)

## EE 364M: Mathematics of Convexity

This course covers the elegant mathematical underpinnings of convex optimization, with a focus on those analytic techniques central to the successes of the field. Topics include, but are not limited to, convex sets and functions, separation theorems, duality, set-valued analysis, and the mathematical insights central to the development of modern optimization methods. Pre- or co-requisite:
EE364A, and mathematical analysis at the level of
MATH171.

Last offered: Winter 2024

## MATH 276: Mathematical Problems in Machine Learning (STATS 375)

Mathematical tools to understand modern machine learning systems. Generalization in machine learning, the classical view: uniform convergence, Radamacher complexity. Generalization from stability. Implicit (algorithmic) regularization. Infinite-dimensional models: reproducing kernel Hilbert spaces. Random features approximations to kernel methods. Connections to neural networks, and neural tangent kernel. Nonparametric regression. Asymptotic behavior of wide neural networks. Properties of convolutionalnetworks. Prerequisites: EE364A or equivalent; Stat310A or equivalent. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.

Last offered: Spring 2024

## STATS 375: Mathematical Problems in Machine Learning (MATH 276)

Mathematical tools to understand modern machine learning systems. Generalization in machine learning, the classical view: uniform convergence, Radamacher complexity. Generalization from stability. Implicit (algorithmic) regularization. Infinite-dimensional models: reproducing kernel Hilbert spaces. Random features approximations to kernel methods. Connections to neural networks, and neural tangent kernel. Nonparametric regression. Asymptotic behavior of wide neural networks. Properties of convolutionalnetworks. Prerequisites: EE364A or equivalent; Stat310A or equivalent. NOTE: Undergraduates require instructor permission to enroll. Undergraduates interested in taking the course should contact the instructor for permission, providing information about relevant background such as performance in prior coursework, reading, etc.

Last offered: Spring 2024

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