add a few convex models

src/OptimizationProblems.jl

@@ -2,8 +2,12 @@ module OptimizationProblems
 
 using JuMP
 
+include("arglina.jl")
+include("arglinb.jl")
+include("arglinc.jl")
 include("arwhead.jl")
 include("bdqrtic.jl")
+include("brownden.jl")
 include("broydn7d.jl")
 include("brybnd.jl")
 include("chainwoo.jl")
@@ -30,13 +34,15 @@ include("freuroth.jl")
 include("genhumps.jl")
 include("indef_mod.jl")
 include("liarwhd.jl")
+include("meyer3.jl")
 include("morebv.jl")
 include("ncb20.jl")
 include("ncb20b.jl")
 include("noncvxu2.jl")
 include("noncvxun.jl")
 include("nondia.jl")
 include("nondquar.jl")
+include("palmer1c.jl")
 include("penalty2.jl")
 include("penalty3.jl")
 include("powellsg.jl")

src/arglina.jl

@@ -0,0 +1,31 @@
+#   Linear function - full rank
+#
+#   Source: Problem 32 in
+#   J.J. More', B.S. Garbow and K.E. Hillstrom,
+#   "Testing Unconstrained Optimization Software",
+#   ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
+#
+#   See also Buckley#80 (with different N and M)
+#
+#   classification SUR2-AN-V-0
+
+export arglina
+
+"Linear function with `n` parameters and `m` observations  - full rank"
+function arglina(n::Int=100, m::Int=200)
+
+  m < n && warn("arglina: must have m ≥ n")
+  m = max(m, n)
+
+  nlp = Model()
+
+  @variable(nlp, x[j=1:n], start=1.0)
+
+  @NLobjective(
+    nlp,
+    Min,
+    sum((x[i] - 2/m * sum(x[j] for j = 1:n) - 1)^2 for i = 1:n) + sum((-2/m * sum(x[j] for j = 1:n) - 1)^2 for i = n+1:m)
+  )
+
+  return nlp
+end

src/arglinb.jl

@@ -0,0 +1,31 @@
+#   Linear function - rank 1
+#
+#   Source: Problem 33 in
+#   J.J. More', B.S. Garbow and K.E. Hillstrom,
+#   "Testing Unconstrained Optimization Software",
+#   ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
+#
+#   See also Buckley#93 (with different N and M)
+#
+#   classification SUR2-AN-V-0
+
+export arglinb
+
+"Linear function with `n` parameters and `m` observations - rank 1"
+function arglinb(n::Int=10, m::Int=20)
+
+  m < n && warn("arglinb: must have m ≥ n")
+  m = max(m, n)
+
+  nlp = Model()
+
+  @variable(nlp, x[j=1:n], start=1.0)
+
+  @NLobjective(
+    nlp,
+    Min,
+    sum((i * sum(j * x[j] for j = 1:n) - 1)^2 for i = 1:m)
+  )
+
+  return nlp
+end

src/arglinc.jl

@@ -0,0 +1,31 @@
+#   Linear function - rank 1, zero columns and rows
+#
+#   Source: Problem 34 in
+#   J.J. More', B.S. Garbow and K.E. Hillstrom,
+#   "Testing Unconstrained Optimization Software",
+#   ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
+#
+#   See also Buckley#101 (with different N and M)
+#
+#   classification SUR2-AN-V-0
+
+export arglinc
+
+"Linear function with `n` parameters and `m` observations - rank 1, zero columns and rows"
+function arglinc(n::Int=10, m::Int=20)
+
+  m < n && warn("arglinc: must have m ≥ n")
+  m = max(m, n)
+
+  nlp = Model()
+
+  @variable(nlp, x[j=1:n], start=1.0)
+
+  @NLobjective(
+    nlp,
+    Min,
+    2 + sum(((i-1) * sum(j * x[j] for j = 2:n-1) - 1)^2 for i = 2:m-1)
+  )
+
+  return nlp
+end

src/brownden.jl

@@ -0,0 +1,35 @@
+#   Brown and Dennis function
+#
+#   Source: Problem 16 in
+#   J.J. More', B.S. Garbow and K.E. Hillstrom,
+#   "Testing Unconstrained Optimization Software",
+#   ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
+#
+#   See also Buckley#30
+#
+#   classification SUR2-AN-4-0
+
+export brownden
+
+"Brown and Dennis function"
+function brownden(m::Int=20)
+
+  m < 4 && warn("brownden: must have m ≥ 4")
+  m = max(m, 4)
+
+  nlp = Model()
+
+  x0 = [25.0, 5, -5, -1]
+
+  @variable(nlp, x[j=1:4], start=x0[j])
+
+  t = Float64[i/5 for i = 1:m]
+
+  @NLobjective(
+    nlp,
+    Min,
+    sum(((x[1] + t[i] * x[2] - exp(t[i]))^2 + (x[3] + x[4] * sin(t[i]) - cos(t[i]))^2)^2 for i = 1:m)
+  )
+
+  return nlp
+end

src/meyer3.jl

@@ -0,0 +1,36 @@
+#   Meyer function
+#
+#   Source:  Problem 10 in
+#   J.J. More', B.S. Garbow and K.E. Hillstrom,
+#   "Testing Unconstrained Optimization Software",
+#   ACM Transactions on Mathematical Software, vol. 7(1), pp. 17-41, 1981.
+#
+#   See also Buckley #29 (p. 73).
+#
+#   classification SUR2-RN-3-0
+
+export meyer3
+
+"Meyer function"
+function meyer3()
+
+  nlp = Model()
+
+  x0 = [0.02, 4000, 250]
+
+  @variable(nlp, x[j=1:3], start=x0[j])
+
+  y = [34780, 28610, 23650, 19630, 16370, 13720, 11540, 9744, 8261, 7030, 6005,
+  5147, 4427, 3820, 3307, 2872]
+
+  t = 45 + 5 * (1:16)
+
+  @NLobjective(
+    nlp,
+    Min,
+    sum((x[1] * exp(x[2]/(t[i] + x[3])) - y[i])^2 for i = 1:16)
+  )
+
+  return nlp
+
+end

src/palmer1c.jl

@@ -0,0 +1,43 @@
+#   A linear least squares problem
+#   arising from chemical kinetics.
+#
+#   model: H-N=N=N TZVP+MP2
+#   fitting Y to A0 + A2 X**2 + A4 X**4 + A6 X**6 + A8 X**8 +
+#                A10 X**10 + A12 X**12 + A14 X**14
+#
+#   Source:
+#   M. Palmer, Edinburgh, private communication.
+#
+#   classification QUR2-RN-8-0
+
+export palmer1c
+
+"A linear least squares problem arising from chemical kinetics."
+function palmer1c()
+
+  nlp = Model()
+
+  @variable(nlp, x[j=1:8], start=1.0)
+
+  X = [-1.788963, -1.745329, -1.658063, -1.570796, -1.483530,  -1.396263,
+       -1.308997, -1.218612, -1.134464, -1.047198, -0.872665,  -0.698132, -0.523599,
+       -0.349066, -0.174533,  0.0000000, 1.788963,  1.745329,   1.658063,  1.570796,
+        1.483530,  1.396263,  1.308997,  1.218612,  1.134464,   1.047198,  0.872665,
+        0.698132,  0.523599,  0.349066,  0.174533, -1.8762289, -1.8325957, 1.8762289,
+        1.8325957]
+
+  Y = [ 78.596218, 65.77963,   43.96947, 27.038816, 14.6126,    6.2614,  1.538330,
+         0.000000,   1.188045,  4.6841,  16.9321,   33.6988,   52.3664, 70.1630,   83.4221,
+        88.3995,   78.596218,  65.77963, 43.96947,  27.038816, 14.6126,  6.2614,    1.538330,
+         0.000000,  1.188045,   4.6841,  16.9321,   33.6988,   52.3664, 70.1630,   83.4221,
+       108.18086,  92.733676, 108.18086, 92.733676]
+
+  @NLobjective(
+    nlp,
+    Min,
+    sum((Y[i] - (x[1] + x[2] * X[i]^2 + x[3] * X[i]^4 + x[4] * X[i]^6 + x[5] * X[i]^8 + x[6] * X[i]^10 + x[7] * X[i]^12 + x[8] * X[i]^14))^2 for i = 1:35)
+  )
+
+  return nlp
+
+end