## CME 364A: Convex Optimization I (EE 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, Sum
| Units: 3

Instructors:
Duchi, J. (PI)
;
Cauchois, M. (TA)
;
Fu, A. (TA)
;
Kim, J. (TA)
;
Luxenberg, E. (TA)
;
Marsden, A. (TA)

## EE 263: Introduction to Linear Dynamical Systems (CME 263)

Applied linear algebra and linear dynamical systems with applications to circuits, signal processing, communications, and control systems. Topics: least-squares approximations of over-determined equations, and least-norm solutions of underdetermined equations. Symmetric matrices, matrix norm, and singular-value decomposition. Eigenvalues, left and right eigenvectors, with dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input/multi-output systems, impulse and step matrices; convolution and transfer-matrix descriptions. Control, reachability, and state transfer; observability and least-squares state estimation. Prerequisites: Linear algebra and matrices as in
ENGR 108 or
MATH 104; ordinary differential equations and Laplace transforms as in
EE 102B or
CME 102.

Terms: Aut
| Units: 3

Instructors:
Lall, S. (PI)
;
Bartan, B. (TA)
;
Lacotte, J. (TA)
;
Lee, C. (TA)
;
Mottaghi, A. (TA)
;
Sinha, R. (TA)
;
Tragus, N. (TA)

## 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:
Duchi, J. (PI)

## EE 373A: Adaptive Signal Processing

Learning algorithms for adaptive digital filters. Self-optimization. Wiener filter theory. Quadratic performance functions, their eigenvectors and eigenvalues. Speed of convergence. Asymptotic performance versus convergence rate. Applications of adaptive filters to statistical prediction, process modeling, adaptive noise canceling, adaptive antenna arrays, adaptive inverse control, and equalization and echo canceling in modems. Artificial neural networks. Cognitive memory/human and machine. Natural and artificial synapses. Hebbian learning. The Hebbian-LMS algorithm. Theoretical and experimental research projects in adaptive filter theory, communications, audio systems, and neural networks. Biomedical research projects, supervised jointly by EE and Medical School faculty. Recommended:
EE263,
EE264,
EE278.

Terms: Spr
| Units: 3

Instructors:
Widrow, B. (PI)

## EE 378B: Inference, Estimation, and Information Processing

Techniques and models for signal, data and information processing, with emphasis on incomplete data, non-ordered index sets and robust low-complexity methods. Linear models; regularization and shrinkage; dimensionality reduction; streaming algorithms; sketching; clustering, search in high dimension; low-rank models; principal component analysis. Applications include: positioning from pairwise distances; distributed sensing; measurement/traffic monitoring in networks; finding communities/clusters in networks; recommendation systems; inverse problems. Prerequisites: EE278 and EE263 or equivalent. Recommended but not required:
EE378A

Terms: Win
| Units: 3

Instructors:
Montanari, A. (PI)

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