5 files changed, 38 insertions, 6 deletions

diff --git a/packages/glpk/examples/simplex1.hs b/packages/glpk/examples/simplex1.hs
index e7aeaa9..a326555 100644
--- a/packages/glpk/examples/simplex1.hs
+++ b/packages/glpk/examples/simplex1.hs
@@ -9,9 +9,9 @@ constr = Dense [ [1,1,1]  :<=: 100
                , [2,2,6]  :<=: 300 ]
 
 -- default bounds
-bnds = [ 1 :=>: 0
-       , 2 :=>: 0
-       , 3 :=>: 0 ]
+bnds = [ 1 :>=: 0
+       , 2 :>=: 0
+       , 3 :>=: 0 ]
 
 main = do
     print $ simplex objFun constr []
diff --git a/packages/glpk/examples/simplex2.hs b/packages/glpk/examples/simplex2.hs
index f4e27fd..0d83ca9 100644
--- a/packages/glpk/examples/simplex2.hs
+++ b/packages/glpk/examples/simplex2.hs
@@ -10,9 +10,14 @@ constr2 = Dense [ [2,1,0] :<=: 10
                 , [0,1,5] :<=: 20
                 ]
 
+constr3 = General [ [1#1, 1#1, 1#2] :<=: 10
+                  , [1#2, 5#3] :<=: 20
+                  ]
+
 main = do
     print $ simplex prob constr1 []
     print $ simplex prob constr2 []
-    print $ simplex prob constr2 [ 2 :=>: 1, 3 :&: (2,7)]
+    print $ simplex prob constr3 []
+    print $ simplex prob constr2 [ 2 :>=: 1, 3 :&: (2,7)]
     print $ simplex prob constr2 [ Free 2 ]
 
diff --git a/packages/glpk/examples/simplex3.hs b/packages/glpk/examples/simplex3.hs
index e093124..0997320 100644
--- a/packages/glpk/examples/simplex3.hs
+++ b/packages/glpk/examples/simplex3.hs
@@ -11,7 +11,7 @@ constr = Dense
     , [0.03, 0.05, 0.08, 0.02, 0.06, 0.01, 0]    :<=:  100
     , [0.02, 0.04, 0.01, 0.02, 0.02, 0,    0]    :<=:  40
     , [0.02, 0.03, 0,    0,    0.01, 0,    0]    :<=:  30
-    , [0.7,  0.75, 0.8,  0.75, 0.8,  0.97,  0]   :=>:  1500
+    , [0.7,  0.75, 0.8,  0.75, 0.8,  0.97,  0]   :>=:  1500
     , [0.02, 0.06, 0.08, 0.12, 0.02, 0.01, 0.97] :&: (250,300)
     ]
 
diff --git a/packages/glpk/examples/simplex4.hs b/packages/glpk/examples/simplex4.hs
index 9a205ad..22b131c 100644
--- a/packages/glpk/examples/simplex4.hs
+++ b/packages/glpk/examples/simplex4.hs
@@ -11,7 +11,7 @@ constr = Sparse
     , [0.03#1, 0.05#2, 0.08#3, 0.02#4, 0.06#5, 0.01#6]       :<=: 100
     , [0.02#1, 0.04#2, 0.01#3, 0.02#4, 0.02#5]               :<=:  40
     , [0.02#1, 0.03#2, 0.01#5]                               :<=:  30
-    , [0.7#1,  0.75#2, 0.8#3,  0.75#4, 0.8#5,  0.97#6]       :=>:  1500
+    , [0.7#1,  0.75#2, 0.8#3,  0.75#4, 0.8#5,  0.97#6]       :>=:  1500
     , [0.02#1, 0.06#2, 0.08#3, 0.12#4, 0.02#5, 0.01#6, 0.97#7] :&: (250,300)
     ]
 
diff --git a/packages/glpk/examples/simplex5.hs b/packages/glpk/examples/simplex5.hs
new file mode 100644
index 0000000..ecbcdaa
--- /dev/null
+++ b/packages/glpk/examples/simplex5.hs
@@ -0,0 +1,27 @@
+import Numeric.LinearProgramming
+
+-- This is a linear program from the paper "Picking vs. Guessing Secrets: A Game-theoretic Analysis"
+
+gamma = 100000 :: Double
+sigma = 1 :: Double
+n = 64 :: Int
+cost_fun :: Int -> Double
+cost_fun i = (fromIntegral i) / (fromIntegral n)
+size_fun :: Int -> Double
+size_fun i = 2^(fromIntegral i)
+
+prob = Minimize $ map cost_fun [1..n]
+bnds = [i :&: (0,1) | i <- [1..n]]
+
+constr1 = [[1 # i | i <- [1..n]] :==: 1] ++
+          [[1/(size_fun i) # i,
+            -1/(size_fun (i+1)) # i+1] :>=: 0 | i <- [1..n-1]] ++
+          [(
+            [gamma#i | i <- [1..k]] ++
+            (concat [[sigma*(size_fun i) # j | j <- [1..i-1]] | i <- [1..k]]) ++
+            [((size_fun i) - 1)/2 # i | i <- [1..k]])
+           :<=: (sigma * (foldr (+) 0 (map size_fun [1..k]))) | k <- [1..n]]
+
+main = do
+  print $ simplex prob (General constr1) bnds -- NoFeasible
+  print $ exact   prob (General constr1) bnds -- solution found