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Revision as of 17:04, 4 May 2015
Contents
Catalog Information
Title
Algorithms Design and Optimization 1
(Credit Hours:Lecture Hours:Lab Hours)
(3:3:0)
Offered
F
Prerequisite
Math 290, Math 313, Math 314, Math 341; concurrent with Math 321, Math 334, Math 344
Description
A treatment of algorithms used to solve these problems. Specific topics include Complexity and Data, Approximation Theory, Recursive Algorithms, Linear Optimization, Unconstrained Optimization, Constrained Optimization, Global Optimization.
Desired Learning Outcomes
Prerequisites
Math 290, Math 313, Math 314, Math 341; concurrent with Math 321, Math 334, Math 344
Minimal learning outcomes
Students will have a solid understanding of the concepts listed below. They will be able to prove many of the theorems that are central to this material. They will understand the model specifications for the optimization algorithms, and be able to recognize whether they apply to a given application or not. They will be able to perform the relevant computations on small, simple problems. They will be able to describe the optimization and approximation algorithms well enough that they could program simple versions of them, and will have a basic knowledge of the computational strengths and weaknesses of the algorithms covered.
 Complexity and Data
 Asymptotic Analysis
 Combinatorics
 Graphs and Trees
 Complexity (P, NP, NP Complete)
 Approximation Theory
 Interpolation and Splines
 StoneWeierstrass Theorem
 Bezier Curves
 BSplines
 Recursive Algorithms
 Difference Calculus, including Summation by Parts
 Simple linear recurrences
 General linear recurrences
 Generating functions
 Linear Optimization
 Problem Formulation
 Simplex Method
 Duality
 Applications
 Unconstrained Optimization
 Steepest Descent
 Newton
 Broyden
 Conjugate Gradient
 Applications
 Constrained Optimization
 Equality Constrained, Lagrange Multipliers
 Inequality Constrained, KKT Condition
 Applications
 Global Optimization
 Interior Point Methods
 Genetic Algorithms
 Simulated Annealing
Textbooks
Possible textbooks for this course include (but are not limited to):