171 - 180 of 236 results for: MS

This experiential learning course explores why entrepreneurial efforts inside governments succeed or fail. For students interested in entrepreneurship, this setting offers one of the most demanding environments for building and scaling new organizations. This topic matters because government innovation shapes public outcomes, national security, and long-term technological competitiveness. Over the last decade, the U.S. government has created more than 100 innovation organizations such as digital service teams and rapid capability offices to advance emerging technologies. Yet while some of these "government startups" achieve meaningful breakthroughs, others stall without widely understood reasons, revealing how little is known about entrepreneurship inside government. Students learn how to overcome organizational inertia, build legitimacy, navigate resource dependencies, establish effective governance, and structure organizations that can adapt and pivot. Together, these principles form a practical framework for improving performance. Each team studies a real government exploratory unit, essentially a startup inside the public sector, and explains its performance using course concepts. Student teams conduct rigorous research grounded in external interviews and produce publicly available reports with recommendations for relevant agencies. The course is intended for graduate and undergraduate students interested in entrepreneurship, national security, public policy, emerging technologies, and innovation. No prior government experience is required. Admission is by application.

Prerequisite: doctoral candidacy.

Each course session will be devoted to a specific MS&E PhD research area. Advanced students will make presentations designed for first-year doctoral students regardless of area. The presentations will be devoted to: illuminating how people in the area being explored that day think about and approach problems, and illustrating what can and cannot be done when addressing problems by deploying the knowledge, perspectives, and skills acquired by those who specialize in the area in question. Area faculty will attend and participate. During the last two weeks of the quarter groups of first year students will make presentations on how they would approach a problem drawing on two or more of the perspectives to which they have been exposed earlier in the class. Attendance is mandatory and performance will be assessed on the basis of the quality of the students' presentations and class participation. Restricted to first year MS&E PhD students.

Formulation of standard linear programming models. Theory of polyhedral convex sets, linear inequalities, alternative theorems, and duality. Variants of the simplex method and the state of art interior-point algorithms. Sensitivity analyses, economic interpretations, and primal-dual methods. Relaxations of harder optimization problems and recent convex conic linear programs. Applications include game equilibrium facility location. Prerequisite: MATH 113 or consent of instructor.

Optimization entails seeking decisions that maximize objectives while satisfying constraints, with applications across engineering, business, economics, statistics, data analysis, and everyday life. This course provides an in-depth and rigorous introduction to mathematical optimization, covering how to formulate, analyze, and solve real-world problems using modern optimization theory and software. Topics include finite-dimensional linear optimization problems with continuous and discrete variables, sensitivity and duality, basic elements of convex analysis, first- and second-order optimality conditions for nonlinear optimization problems, and a discussion of important algorithmic and computational aspects related to optimization. Prerequisites: MATH 113, 115, or equivalent.

Fundamental theory for solving continuous optimization problems with provable efficiency guarantees. Coverage of both canonical optimization methods and techniques, e.g. gradient descent, mirror descent, stochastic methods, acceleration, higher-order methods, etc. and canonical optimization problems, critical point computation for non-convex functions, smooth-convex function minimization, regression, linear programming, etc. Focus on provable rates for solving broad classes of prevalent problems including both classic problems and those motivated by large-scale computational concerns. Discussion of computational ramifications, fundamental information-theoretic limits, and problem structure. Prerequisite: linear algebra, multivariable calculus, probability, and proofs.

Algorithms, algorithmic paradigms, and algorithmic tools for provably solving combinatorial optimization problems. Emphasis on graph optimization and discussion of approaches based on linear programming and continuous optimization. Potential optimization problems include both polynomial time solve-able problems, e.g., maximum flow, minimum cost flow, matching, assignment, minimum cut, matroid optimization, submodular function minimization, and NP-hard problems, e.g., Steiner trees, traveling salesperson, maximum cut. Potential paradigms and tools include: linear programming, multiplicative weight update method, algebraic methods, and spectral methods. Prerequisite: 161 or equivalent.

How can we design AI systems that are not only powerful but also provably safe and trustworthy? This advanced PhD seminar surveys algorithmic methods to enforce hard constraints in machine learning, reinforcement learning, and generative AI. Topics include classical constrained optimization (Lagrangian methods, robust and stochastic programming), safe reinforcement learning (trust regions, Lyapunov functions, reachability, shielding), hybrid ML-optimization methods (projection networks, solver-in-the-loop architectures), and alignment strategies for large language models (fine-tuning, model editing, tool use, and interactive alignment). Each week highlights a key theoretical result alongside state-of-the-art research, with applications spanning robotics, finance, healthcare, energy, and language models. Students will critically assess the strengths and limitations of these methods and develop final projects that apply or extend them in real-world domains. Prerequisites: optimization at the level of CME 307 or EE 364a.

The theory of matching with its roots in the work of mathematical giants like Euler and Kirchhoff has played a central and catalytic role in combinatorial optimization for decades. More recently, the growth of online marketplaces for allocating advertisements, rides, or other goods and services has led to new interest and progress in this area. The course starts with classic results characterizing matchings in bipartite and general graphs and explores connections with other branches of mathematics, including game theory and algebraic graph theory. Those results are complemented with models and algorithms developed for modern applications in market design, online advertising, and ride sharing. May be repeated for credit. Prerequisite: 212, CS 261, or equivalent.