C S 412
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Linear Programming and Convex Optimization
Computer ScienceCollege of Computational, Mathematical, & Physical Sciences
Course Description
Optimization, problem formulation, and solution algorithms, including simplex and interior point methods. Applications from control, data mining, finance, game theory, learning, network flow, operations research, and statistical estimation.
When Taught
Contact Department
Min
3
Fixed/Max
3
Fixed
3
Fixed
0
Prerequisite
Complete ALL of the following Courses:
- 13764-000
AND 13765-000
Other Prerequisites
or instructor's consent.
Title
Mathematical Foundations
Learning Outcome
Develop a fluency in the mathematical foundations needed to pose optimization problems, including an appreciation for the role of convexity in characterizing solvable problems. This rigorous conceptualizing is intellectually enlarging, training the mind to identify the structured, solvable essence within complex situations.
Title
Simplex Method
Learning Outcome
Develop a fluency with the Simplex Method as a solution technique to Linear Programming problems. Understand how it exploits the linear nature of the problem to yield good average-case performance while failing to be efficient in the worst-case. Navigating these computational realities is character building, as it requires the meticulous logic and persistence to handle large-scale data with total accuracy.
Title
Duality Theory
Learning Outcome
Understand the meaning of weak and strong duality and their role in the design and verification of algorithmic solutions to optimization problems. Students will find this exploration spiritually strengthening as they observe the inherent balance and profound symmetry that governs mathematical truth.
Title
Sensitivity Analysis
Learning Outcome
Be able to characterize how to perturb the data of an existing problem so that its solution remains optimal for the new, perturbed problem. Developing this predictive foresight fosters a capacity for lifelong learning, enabling students to adapt their strategies as environments and information evolve.
Title
Interior Point Methods
Learning Outcome
Develop a fluency with interior point methods for solving Linear Programming problems and understand how these solutions may be extended to solve nonlinear, convex optimization problems. Expanding one's technical repertoire in this way is intellectually enlarging, providing a more comprehensive understanding of the universal principles of optimization.
Title
Applications
Learning Outcome
Explore the role of Linear and Convex Programming in a variety of applications, including 1) Finance, 2) Game Theory, 3) Regression, and 4) Computer Networking. This practical application of high-level theory is a form of stewardship, preparing students to use their specialized talents in meaningful service to their professions and communities.
