-
Notifications
You must be signed in to change notification settings - Fork 23
/
mpec1.jl
143 lines (117 loc) · 5.16 KB
/
mpec1.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
#*******************************************************/
#* Copyright(c) 2018 by Artelys */
#* This source code is subject to the terms of the */
#* MIT Expat License (see LICENSE.md) */
#*******************************************************/
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This example demonstrates how to use Knitro to solve the following
# simple mathematical program with equilibrium/complementarity
# constraints(MPEC/MPCC).
#
# min (x0 - 5)^2 +(2 x1 + 1)^2
# s.t. -1.5 x0 + 2 x1 + x2 - 0.5 x3 + x4 = 2
# x2 complements(3 x0 - x1 - 3)
# x3 complements(-x0 + 0.5 x1 + 4)
# x4 complements(-x0 - x1 + 7)
# x0, x1, x2, x3, x4 >= 0
#
# The complementarity constraints must be converted so that one
# nonnegative variable complements another nonnegative variable.
#
# min (x0 - 5)^2 +(2 x1 + 1)^2
# s.t. -1.5 x0 + 2 x1 + x2 - 0.5 x3 + x4 = 2 (c0)
# 3 x0 - x1 - 3 - x5 = 0 (c1)
# -x0 + 0.5 x1 + 4 - x6 = 0 (c2)
# -x0 - x1 + 7 - x7 = 0 (c3)
# x2 complements x5
# x3 complements x6
# x4 complements x7
# x0, x1, x2, x3, x4, x5, x6, x7 >= 0
#
# The solution is(1, 0, 3.5, 0, 0, 0, 3, 6), with objective value 17.
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
using KNITRO, Test
function example_mpec1(; verbose=true)
# Create a new Knitro solver instance.
kc = KNITRO.KN_new()
# Illustrate how to override default options by reading from
# the knitro.opt file.
options = joinpath(dirname(@__FILE__), "..", "examples", "knitro.opt")
KNITRO.KN_load_param_file(kc, options)
# Initialize Knitro with the problem definition.
# Add the variables and set their bounds and initial values.
# Note: unset bounds assumed to be infinite.
KNITRO.KN_add_vars(kc, 8)
KNITRO.KN_set_var_lobnds_all(kc, zeros(Float64, 8))
KNITRO.KN_set_var_primal_init_values_all(kc, zeros(Float64, 8))
# Add the constraints and set their bounds.
KNITRO.KN_add_cons(kc, 4)
KNITRO.KN_set_con_eqbnds_all(kc, Float64[2, 3, -4, -7])
# Add coefficients for all linear constraints at once.
# c0
lconIndexCons = Int32[0, 0, 0, 0, 0]
lconIndexVars = Int32[0, 1, 2, 3, 4]
lconCoefs = [-1.5, 2.0, 1.0, -0.5, 1.0]
# c1
lconIndexCons = [lconIndexCons; Int32[1, 1, 1]]
lconIndexVars = [lconIndexVars; Int32[0, 1, 5]]
lconCoefs = [lconCoefs; [3.0, -1.0, -1.0]]
# c2
lconIndexCons = [lconIndexCons; Int32[2, 2, 2]]
lconIndexVars = [lconIndexVars; Int32[0, 1, 6]]
lconCoefs = [lconCoefs; [-1.0, 0.5, -1.0]]
# c3
lconIndexCons = [lconIndexCons; Int32[3, 3, 3]]
lconIndexVars = [lconIndexVars; Int32[0, 1, 7]]
lconCoefs = [lconCoefs; [-1.0, -1.0, -1.0]]
KNITRO.KN_add_con_linear_struct(kc, lconIndexCons, lconIndexVars, lconCoefs)
# Note that the objective(x0 - 5)^2 +(2 x1 + 1)^2 when
# expanded becomes:
# x0^2 + 4 x1^2 - 10 x0 + 4 x1 + 26
# Add quadratic coefficients for the objective
qobjIndexVars1 = Int32[0, 1]
qobjIndexVars2 = Int32[0, 1]
qobjCoefs = [1.0, 4.0]
KNITRO.KN_add_obj_quadratic_struct(kc, qobjIndexVars1, qobjIndexVars2, qobjCoefs)
# Add linear coefficients for the objective
lobjIndexVars = Int32[0, 1]
lobjCoefs = [-10.0, 4.0]
KNITRO.KN_add_obj_linear_struct(kc, lobjIndexVars, lobjCoefs)
# Add constant to the objective
KNITRO.KN_add_obj_constant(kc, 26.0)
# Set minimize or maximize(if not set, assumed minimize)
KNITRO.KN_set_obj_goal(kc, KNITRO.KN_OBJGOAL_MINIMIZE)
# Now add the complementarity constraints
ccTypes = [KNITRO.KN_CCTYPE_VARVAR, KNITRO.KN_CCTYPE_VARVAR, KNITRO.KN_CCTYPE_VARVAR]
indexComps1 = Int32[2, 3, 4]
indexComps2 = Int32[5, 6, 7]
KNITRO.KN_set_compcons(kc, 3, ccTypes, indexComps1, indexComps2)
kn_outlev = verbose ? KNITRO.KN_OUTLEV_ALL : KNITRO.KN_OUTLEV_NONE
KNITRO.KN_set_param(kc, KNITRO.KN_PARAM_OUTLEV, kn_outlev)
# Solve the problem.
#
# Return status codes are defined in "knitro.h" and described
# in the Knitro manual.
nStatus = KNITRO.KN_solve(kc)
# An example of obtaining solution information.
nStatus, objSol, x, lambda_ = KNITRO.KN_get_solution(kc)
if verbose
println("Knitro converged with final status = ", nStatus)
println(" optimal objective value = ", objSol)
println(" optimal primal values x0=", x[1])
println(" x1=", x[2])
println(" x2=", (x[3], x[6]))
println(" x3=", (x[4], x[7]))
println(" x4=", (x[5], x[8]))
println(" feasibility violation = ", KNITRO.KN_get_abs_feas_error(kc))
println(" KKT optimality violation = ", KNITRO.KN_get_abs_opt_error(kc))
end
# Delete the Knitro solver instance.
KNITRO.KN_free(kc)
@testset "Example MPEC 1" begin
@test nStatus == 0
@test objSol ≈ 17.0
@test x ≈ [1.0, 0.0, 3.5, 0.0, 0.0, 0.0, 3.0, 6.0]
end
end
example_mpec1(; verbose=isdefined(Main, :KN_VERBOSE) ? KN_VERBOSE : true)