13 Optimization

13 Optimization - Optimization CEE 3804 Computer...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
Optimization CEE 3804 Computer Applications for Civil and Environmental Engineers
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
CEE 3804 2 Optimization While root finding involves searching for zeros of a function, optimization involves searching for a maximum or minimum of a function. An optimum occurs where the curve is flat. Hence f’(x) = 0 at an optimum. The second derivative f’’(x) is positive for a minimum and negative for a maximum.
Background image of page 2
CEE 3804 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
CEE 3804 4 Types of Optimization Some optimization algorithms treat the problem as a root finding problem for f’(x). As with roots, a distinction is made between single variable problems and multivariable problems.
Background image of page 4
CEE 3804 5 Types of Optimization Problems Optimization problems can be either Unconstrained – no limits are placed on the allowable answers Constrained - additional equations limit the acceptable response region. If the equation to be optimized is linear, and the constraints are linear, the optimization is called linear programming
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
CEE 3804 6 Objective Function Is a single value function of the set of control variables or the control vector x. A mathematical statement of the goal and a measure of how effective the goal is met. The objective function may be either maximized or minimized.
Background image of page 6
CEE 3804 7 Control or Decision Variables Term used to designate any parameter that may vary in the design, planning or management process. May be discrete or continuous.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
CEE 3804 8 Constraint Equations Mathematical equation expressing limitations placed on the problem. Constraints may be stated as strict equality or as inequality
Background image of page 8
CEE 3804 9 Feasible Solutions A feasible solution is any combination that satisfies the set of constraint equations. A solution that does not satisfy all the constraint equations is termed infeasible.
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
CEE 3804 10 Optimal Solution A feasible solution that optimizes the objective function is called the optimal solution.
Background image of page 10
CEE 3804 11 Global and Local Optimum Just as with multiple roots, an optimization problem can have several optimum.
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/14/2008 for the course CEE 3804 taught by Professor Aatrani during the Fall '07 term at Virginia Tech.

Page1 / 42

13 Optimization - Optimization CEE 3804 Computer...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online