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Course Criteria
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4.00 Credits
Introduction to linear optimization and its extensions emphasizing both methodology and the underlying mathematical structures and geometrical ideas. Covers classical theory of linear programming as well as some recent advances in the field. Topics: simplex method; duality theory; sensitivity analysis; network flow problems; decomposition; integer programming; interior point algorithms for linear programming; and introduction to combinatorial optimization and NP-completeness.
Prerequisite:
Prereq: 18.06
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3.00 Credits
Focuses on network models for industrial logistics systems, transportation systems, communication systems, and other applications. Emphasizes a rigorous treatment of algorithms and their efficiency. Covers algorithms for shortest paths, maximum flows, minimum cost flows, and network design, as well as implementation issues.
Prerequisite:
Prereq: 6.046, 15.081, or permission of instructor
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3.00 Credits
In-depth treatment of the modern theory of integer programming and combinatorial optimization, emphasizing geometry, duality and algorithms. Topics include formulating problems in integer variables, enhancement of formulations, ideal formulations, integer programming duality, linear and semidefinite relaxations, lattices and their applications, the geometry of integer programming, primal methods, cutting plane methods, connections with algebraic geometry, computational complexity, approximation algorithms, heuristic and enumerative algorithms, mixed integer programming and solutions of large scale problems.
Prerequisite:
Prereq: 15.081J or permission of instructor
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4.00 Credits
A unified analytical and computational approach to nonlinear optimization problems. Unconstrained optimization methods include gradient, conjugate direction, Newton, and quasi-Newton methods. Constrained optimization methods include feasible directions, projection, interior point, and Lagrange multiplier methods. Convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. Comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory. Applications drawn from control, communications, power systems, and resource allocation problems.
Prerequisite:
Prereq: 18.06, 18.100
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4.00 Credits
Introduction to probability theory. Probability spaces and measures. Discrete and continuous random variables. Conditioning and independence. Multivariate normal distribution. Abstract integration, expectation, and related convergence results. Moment generating and characteristic functions. Bernoulli and Poisson process. Finite-state Markov chains. Convergence notions and their relations. Limit theorems. Familiarity with elementary notions in probability and real analysis is desirable.
Prerequisite:
Prereq: Calculus II (GIR)
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4.00 Credits
Introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis on methodology and the underlying mathematical structures. Topics include the simplex method, network flow methods, branch and bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton's method, heuristic methods, and dynamic programming and optimal control methods.
Prerequisite:
Prereq: 18.06
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0.00 - 6.00 Credits
Group study of current topics related to operations research/statistics.
Prerequisite:
Prereq: Permission of instructor
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2.00 Credits
Doctoral student seminar covering current topics in applied probability and stochastic processes.
Prerequisite:
Prereq: 6.431
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0.00 - 6.00 Credits
Doctoral student seminar covering current topics related to operations research.
Prerequisite:
Prereq: 15.081J
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2.00 Credits
Clinical trials have become one of the leading barriers to sucess in the introduction of new products and services for the healthcare industry. Subject enables healthcare managers to ask the important questions surrounding a decision to pursue a clinical trial. Deciding to participate in a clinical trial can sometimes result in expensive, long-term corporate commitments, which can have a significant impact on the company's success or failure, particularly in the case of smaller companies. Subject explores issues related to determing whether a clinical trial is needed to significantly further the important goals of the company. Topics include the design, implementation, analysis and presentation of clinical trials. Case scenarios are presented by professionals in the field, and students are asked to develop their own outline plan and clinical trial study plan from the sample cases provided. Enrollment limited.
Prerequisite:
Prereq: None
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