CLASSROOM TUTORIALS
Following is a list of Mathematica
tutorials that are used to supplement lectures throughout the semester. Students are encouraged to go through
these tutorials after each lecture and try their own variations of the
examples.
NOTE: For those who have Mathematica
installed on their machines, clicking any of the .nb links should start up the
local Mathematica program automatically.
If it does not, see your system administrator or web browser
documentation for adding Mathematica to your browser's helper applications.
- This tutorial is to
demonstrate the use of Mathematica and Mathematica graphics
as a classroom teaching and tutorial environment.
Tutorial-01.nb:
- Mathematical formulation of
design optimization problems.
Definition of design variables, objective functions, and
constraints in terms of Mathematica lists and functions.
Tutorial-02.nb:
- Graphical solution of 2-D
optimization problems using Mathematica graphics, and Mathematica
Solve function.
Tutorial-03.nb:
- Example of a two objective
optimization problem, and Pareto optimal curve.
Tutorial-04.nb:
- Fundamental concepts of
optimality. Taylor series
expansion, Gradient vector, Hessian matrix, Quadratic forms, and
Eigenvalues of matrices.
Tutorial-05.nb:
- Fundamental concepts of
optimality-II. Necessary and
sufficient conditions for optimality of unconstrained and equality
constrained problems.
Tutorial-06.nb:
- Fundamental concepts of
optimality-III. Necessary and
sufficient conditions for inequality constrained problems (Kuhn-Tucker
conditions). Post optimality
analysis.
Tutorial-07.nb:
- Linear Programming (LP).
Tutorial-08.nb
:
- Sequential Linear Programming
(SLP) example.
Tutorial-09.nb:
- Implementation of move limits
strategy and use of a Mathematica program for Sequential Linear
Programming,
SequentialLP.m
(see Programs to obtain
a copy).
Tutorial-10.nb:
- One-dimensional unconstrained
minimization. Conversion of
n-D problems to 1-D problems, bracketing the minimum, polynomial
approximation, golden section search, and the use of built-in Mathematica
functions.
Tutorial-11.nb:
- Demonstration of Nelder and
Mead's Sequential Simplex algorithm for unconstrained minimization of
n-dimensional functions. A Mathematica
function called
SequentialSimplex
is included in the package UnconstrainedMin.m (see Programs to obtain a copy).
Tutorial-12.nb:
- Powell's conjugate directions
method for unconstrained minimization of n-dimensional functions. A Mathematica function
ConjugateDirections
is included in the package UnconstrainedMin.m (see Programs to obtain a copy).
Tutorial-13.nb:
- Steepest descent algorithm. A Mathematica function
SteepestDescent
is included in the package UnconstrainedMin.m (see Programs to obtain a copy).
Tutorial-14.nb:
- Fletcher-Reeves conjugate
gradient algorithm. A Mathematica
function
ConjugateGradient
is included in the package UnconstrainedMin.m (see Programs to obtain a copy).
Tutorial-15.nb:
- Newton's method for
unconstrained minimization of n-dimensional functions. A Mathematica function
ConjugateGradient
is included in the package UnconstrainedMin.m (see Programs to obtain a copy).
Tutorial-16.nb:
- Quasi-Newton methods for
unconstrained minimization of n-dimensional functions. A Mathematica function
QuasiNewton
is included in the package UnconstrainedMin.m (see Programs to obtain a copy).
Tutorial-17.nb:
- Penalty function approach for
constrained minimization of n-dimensional functions. A Mathematica function
PenaltyFunction
is included in the package ConstrainedMin.m (see Programs
to obtain a copy).
Tutorial-18.nb:
- Augmented Lagrange multiplier
method and its demonstration for the equality constrained problems and inequality
constrained problems.
Tutorial-19.nb:
- The method of Feasible
Directions, and demonstration of the push-off factor.
Tutorial-20.nb:
- Gradient Projection
method. Computation of
Lagrange multipliers and restoration move.
Tutorial-21.nb:
- THE END
Return to Home page