@@ -135,16 +135,45 @@ We can see that the algorithm quickly converges to the optimal point (see Fig. 5
135135For more examples refer to the python scripts in "examples" folder. [ https://github.com/tsyet12/Duelist-Algorithm-Python/tree/master/examples ]
136136
137137
138- # Small Tutorial on Complex Constraint using Karush-Kuhn-Tucker (KKT) conditions
138+ # Dealing with Complex Constraint using Karush-Kuhn-Tucker (KKT) conditions
139139
140140There will be some problems that have complex constraints. For example, constraints which depends on two or more manipulated variables.
141141
142- Say: we take the same problem from the ** Short Tutorial** , and now we have an extra constraint, which is x1 must be larger than x2:
142+ * Example 1: Inequality*
143+ 144+ Say:
145+ We take the same problem from the ** Short Tutorial** , and now we have an extra constraint, which is x1 must be larger than x2:
146+ 143147> x1>x2
144148
145149Using KKT conditions, we can put this constraint in the objective function:
146150
147- f=(x1,x2) = (x1)^2+(x2)^2 + (
151+ f=(x1,x2) = (x1)^2+(x2)^2 + max(0,x2-x1)
152+ 153+ Implementation:
154+ 155+ ``` python
156+ def f (x1 ,x2 ):
157+ return x1* x1+ x2* x2+ max (0 ,x2- x1)
158+ ```
159+ Continue from Step 2 of ** Short Tutorial** .
160+ 161+ 162+ 163+ * Example 2: Equality*
164+ Say:
165+ We take the same problem from the ** Short Tutorial** , and now the extra constraint is x1 equal to x2:
166+ 167+ f=(x1,x2) = (x1)^2+(x2)^2 + (x2-x1)^2
168+ 169+ Implementation:
170+ 171+ ``` python
172+ def f (x1 ,x2 ):
173+ return x1* x1+ x2* x2+ (x2- x1)* (x2- x1)
174+ ```
175+ 176+ Continue from Step 2 of ** Short Tutorial** .
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150179# Version
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