Specifications

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Quadratic and Linear Programming
Quadratic Programming
Quadratic programming problems involve
minimizing a multivariate quadratic func-
tion subject to linear equality and inequality
constraints. The toolbox implements three
methods for solving these problems: trust-
region, preconditioned conjugate gradient,
and active set.
Trust-region is used for bound constrained
problems.
Preconditioned conjugate gradient is used
for problems subject to equality constraints.
Active set minimizes the objective at each
iteration over the active set (a subset of the
constraints that are locally active) until it
reaches a solution.
Linear Programming
Linear programming problems consist of a
linear expression for the objective function
and linear equality and inequality constraints.
Two methods are used to solve this type of
problem: simplex and interior point.
The interior point method is based on a
primal-dual predictor-corrector algorithm,
and is used for large-scale linear problems.
The simplex method is a systematic proce-
dure for generating and testing candidate
vertex solutions to a linear program.
Binary Integer Programming
Binary integer programming problems
involve minimizing a linear objective func-
tion subject to linear equality and inequality
constraints. Each variable in the optimal
solution must be either a 0 or a 1.
The Optimization Toolbox solves these prob-
lems using a branch-and-bound algorithm that:
• Searches for a feasible binary integer
solution
• Updates the best binary point found as the
search tree grows
• Verifies that no better solution is possible
by solving a series of linear programming
relaxation problems
Required Products
MATLAB
Related Products
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Statistics Toolbox. Apply statistical
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For more information on related products, visit
www.mathworks.com/products/optimization
Platform and System Requirements
For information on platform and system
requirements, visit www.mathworks.com/
products/optimization ■
Tel: [phone] [e-mail] www.mathworks.com
8513v04 06/04
© 2004 by The MathWorks, Inc. MATLAB, Simulink, Stateflow, Handle Graphics, and Real-Time Workshop are registered trademarks, and TargetBox is a trademark of The MathWorks, Inc. Other product or brand names are trademarks or registered trademarks of their respective holders.