L13 Optimization using Excel
• See revised schedule
read 8(1-4) + Excel “help” for Mar 12
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Test Answers
Review: Convex Prog. Prob.
Worksheet modifications
Excel optimization
Summary
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Trendline in Excel
Excel help
“trendline”
for Wed
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Theorem 4.9
Given:
ConstraintSet
S  {x | hi (x )  0, for i  1 to p;
g j (x )  0, j  1 to m}
S is convex if:
1. hi are linear
2. gj are convex i.e. Hg PD or PSD
When f(x) and S are convex=
“convex programming problem”
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“Sufficient” Theorem 4.10, pg 165
The first-order KKT conditions are Necessary
and Sufficient for a GLOBAL minimum….if:
1. f(x) is convex
Hf(x) Positive definite
2. x is defined as a convex feasible set S
Equality constraints must be linear
Inequality constraints must be convex
HINT: linear functions are convex!
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Worksheet Modifications
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Naming cells
Inserting shapes
Inserting MS Equation “object”
Recording macros
Attaching a macro to a shape
Creating a SOLVER hot button
Visual basic, tools/references/solver
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Excel Applications
Figure 6.1 Excel worksheet for finding roots of 2x/3 – sin x :
(a) worksheet; (b) worksheet with formulas showing.
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Solver parameters
Figure 6.2 A Solver Parameters dialog box to
define the problem.
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Figure 6.3 A Solver Results dialog box and the final worksheet.
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Figure 6.4 A Solver Answer Report for roots of 2x/3 – sin x = 0.
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Figure 6.5 Worksheet and Solver Parameters dialog box for
KKT conditions for Example 4.31.
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Figure 6.6 Solver Results for KKT conditions for Example 4.31.
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KKT system of NL EQNs
Prob 4.59 and 4.122
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Figure 6.7 Excel worksheet and Solver Parameters
dialog box for unconstrained problem.
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Constrained Optimization
Prob. 4.69 and 4.122
Min f ( x1 , x2 )  ( x1  3)2  ( x2  3)2
subject t o h  x1  3 x2  1
g  x1  x2  4
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Graphical Solution
x1  3.25
x2  0.75
  1.25
u  0.75  0
s00
f  5.125
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Figure 6.8 Excel worksheet for the linear programming problem.
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Figure 6.9 Solver Parameters dialog box for the linear programming problem.
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Figure 6.10 Solver Results dialog box for the linear programming problem.
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Figure 6.11 Answer Report from Solver for linear programming problem.
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Figure 6.12 Sensitivity Report from Solver for the linear programming problem.
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Figure 6.13 Excel worksheet for the spring design problem.
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Summary
• KKT pt from a Convex Prog. Prob. Is a
global min!
• Use modifications for “ease of use”
• Pay attention to layout
– Design variables
– Parameters
– Analysis/Performance “Variables”
– Objective function
– Constraints
• May need multiple starting points
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