MS&E 312: Advanced Methods in Numerical Optimization (CME 334)
Topics include interiorpoint methods, relaxation methods for nonlinear discrete optimization, sequential quadratic programming methods, optimal control and decomposition methods. Topic chosen in first class; different topics for individuals or groups possible. Individual or team projects. May be repeated for credit.
Terms: Aut

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
MS&E 313: Almost Linear Time Graph Algorithms (CS 269G)
Over the past decade there has been an explosion in activity in designing new provably efficient fast graph algorithms. Leveraging techniques from disparate areas of computer science and optimization researchers have made great strides on improving upon the best known running times for fundamental optimization problems on graphs, in many cases breaking longstanding barriers to efficient algorithm design. In this course we will survey these results and cover the key algorithmic tools they leverage to achieve these breakthroughs. Possible topics include but are not limited to, spectral graph theory, sparsification, oblivious routing, local partitioning, Laplacian system solving, and maximum flow. Prerequisites: calculus and linear algebra.
Terms: Win

Units: 3

Grading: Letter (ABCD/NP)
Instructors:
Sidford, A. (PI)
MS&E 314: Linear and Conic Optimization with Applications (CME 336)
Linear, semidefinite, conic, and convex nonlinear optimization problems as generalizations of classical linear programming. Algorithms include the interiorpoint, barrier function, and cutting plane methods. Related convex analysis, including the separating hyperplane theorem, Farkas lemma, dual cones, optimality conditions, and conic inequalities. Complexity and/or computation efficiency analysis. Applications to combinatorial optimization, sensor network localization, support vector machine, and graph realization. Prerequisite: MS&E 211 or equivalent.
Terms: alternate years, given next year

Units: 3

Grading: Letter or Credit/No Credit
MS&E 316: Discrete Mathematics and Algorithms (CME 305)
Topics: Basic Algebraic Graph Theory, Matroids and Minimum Spanning Trees, Submodularity and Maximum Flow, NPHardness, Approximation Algorithms, Randomized Algorithms, The Probabilistic Method, and Spectral Sparsification using Effective Resistances. Topics will be illustrated with applications from Distributed Computing, Machine Learning, and largescale Optimization. Prerequisites:
CS 261 is highly recommended, although not required.
Terms: Win

Units: 3

Grading: Letter or Credit/No Credit
MS&E 317: Algorithms for Modern Data Models (CS 263)
We traditionally think of algorithms as running on data available in a single location, typically main memory. In many modern applications including web analytics, search and data mining, computational biology, finance, and scientific computing, the data is often too large to reside in a single location, is arriving incrementally over time, is noisy/uncertain, or all of the above. Paradigms such as mapreduce, streaming, sketching, Distributed Hash Tables, Bulk Synchronous Processing, and random walks have proved useful for these applications. This course will provide an introduction to the design and analysis of algorithms for these modern data models. Prerequisite: Algorithms at the level of
CS 261.
Terms: not given this year

Units: 3

Grading: Letter or Credit/No Credit
MS&E 318: LargeScale Numerical Optimization (CME 338)
The main algorithms and software for constrained optimization emphasizing the sparsematrix methods needed for their implementation. Iterative methods for linear equations and least squares. The simplex method. Basis factorization and updates. Interior methods. The reducedgradient method, augmented Lagrangian methods, and SQP methods. Prerequisites: Basic numerical linear algebra, including LU, QR, and SVD factorizations, and an interest in MATLAB, sparsematrix methods, and gradientbased algorithms for constrained optimization. Recommended: MS&E 310, 311, 312, 314, or 315;
CME 108, 200, 302, 304, 334, or 335.
Terms: Spr

Units: 3

Grading: Letter (ABCD/NP)
Instructors:
Saunders, M. (PI)
MS&E 319: Approximation Algorithms
Combinatorial and mathematical programming techniques to derive approximation algorithms for NPhard optimization problems. Prossible topics include: greedy algorithms for vertex/set cover; rounding LP relaxations of integer programs; primaldual algorithms; semidefinite relaxations. May be repeated for credit. Prerequisites: 112 or
CS 161.
Terms: Aut

Units: 3

Repeatable for credit

Grading: Letter or Credit/No Credit
Instructors:
Saberi, A. (PI)
MS&E 321: Stochastic Systems
Topics in stochastic processes, emphasizing applications. Markov chains in discrete and continuous time; Markov processes in general state space; Lyapunov functions; regenerative process theory; renewal theory; martingales, Brownian motion, and diffusion processes. Application to queueing theory, storage theory, reliability, and finance. Prerequisites: 221 or
STATS 217;
MATH 113, 115. (Glynn)
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Blanchet Mancilla, J. (PI)
MS&E 322: Stochastic Calculus and Control
Ito integral, existence and uniqueness of solutions of stochastic differential equations (SDEs), diffusion approximations, numerical solutions of SDEs, controlled diffusions and the HamiltonJacobiBellman equation, and statistical inference of SDEs. Applications to finance and queueing theory. Prerequisites: 221 or
STATS 217:
MATH 113, 115.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Glynn, P. (PI)
MS&E 324: Stochastic Methods in Engineering (CME 308, MATH 228)
The basic limit theorems of probability theory and their application to maximum likelihood estimation. Basic Monte Carlo methods and importance sampling. Markov chains and processes, random walks, basic ergodic theory and its application to parameter estimation. Discrete time stochastic control and Bayesian filtering. Diffusion approximations, Brownian motion and an introduction to stochastic differential equations. Examples and problems from various applied areas. Prerequisites: exposure to probability and background in analysis.
Terms: Spr

Units: 3

Grading: Letter or Credit/No Credit
Instructors:
Glynn, P. (PI)
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