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Instance ann_peaks_exp

Peaks test function learned and optimized by an embedded artificial neural network. In this variant of ann_peaks_tanh, the tanh(x) activation function has been replaced by 1-2/(exp(2x)+1) (form 3 in paper).
Formats gms mod nl osil py
Primal Bounds (infeas ≤ 1e-08)
-6.56303925 p1 ( gdx sol )
(infeas: 2e-15)
Other points (infeas > 1e-08)  
Dual Bounds
-6.56303926 (ANTIGONE)
-6.56369562 (BARON)
-6.56303925 (LINDO)
-6.56311025 (SCIP)
References Schweidtmann, Artur M. and Mitsos, Alexander, Deterministic Global Optimization with Artificial Neural Networks Embedded, Journal of Optimization Theory and Applications, 180:3, 2019, 925-948.
Application Neural Networks
Added to library 29 Nov 2021
Problem type NLP
#Variables 100
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 47
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 1
#Nonlinear Nonzeros in Objective 0
#Constraints 98
#Linear Constraints 51
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 47
Operands in Gen. Nonlin. Functions div exp
Constraints curvature indefinite
#Nonzeros in Jacobian 289
#Nonlinear Nonzeros in Jacobian 47
#Nonzeros in (Upper-Left) Hessian of Lagrangian 47
#Nonzeros in Diagonal of Hessian of Lagrangian 47
#Blocks in Hessian of Lagrangian 47
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 2.2644e-03
Maximal coefficient 9.4928e+00
Infeasibility of initial point 9.714
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*
* Equation counts
*     Total        E        G        L        N        X        C        B
*        99       99        0        0        0        0        0        0
*
* Variable counts
*                  x        b        i      s1s      s2s       sc       si
*     Total     cont   binary  integer     sos1     sos2    scont     sint
*       101      101        0        0        0        0        0        0
* FX      0
*
* Nonzero counts
*     Total    const       NL
*       291      244       47

* Solve m using NLP minimizing objvar;

Variables
    objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,
    x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36,x37,x38,x39,
    x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53,x54,x55,x56,x57,x58,
    x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70,x71,x72,x73,x74,x75,x76,x77,
    x78,x79,x80,x81,x82,x83,x84,x85,x86,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,
    x97,x98,x99,x100,x101;

Equations
    e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19,e20,e21,
    e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36,e37,e38,e39,e40,
    e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53,e54,e55,e56,e57,e58,e59,
    e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70,e71,e72,e73,e74,e75,e76,e77,e78,
    e79,e80,e81,e82,e83,e84,e85,e86,e87,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,
    e98,e99;

e1..  objvar - x53 =E= 0;
e2..  2 / (exp(2 * x55) + 1) + x6 =E= 1;
e3..  2 / (exp(2 * x56) + 1) + x7 =E= 1;
e4..  2 / (exp(2 * x57) + 1) + x8 =E= 1;
e5..  2 / (exp(2 * x58) + 1) + x9 =E= 1;
e6..  2 / (exp(2 * x59) + 1) + x10 =E= 1;
e7..  2 / (exp(2 * x60) + 1) + x11 =E= 1;
e8..  2 / (exp(2 * x61) + 1) + x12 =E= 1;
e9..  2 / (exp(2 * x62) + 1) + x13 =E= 1;
e10..  2 / (exp(2 * x63) + 1) + x14 =E= 1;
e11..  2 / (exp(2 * x64) + 1) + x15 =E= 1;
e12..  2 / (exp(2 * x65) + 1) + x16 =E= 1;
e13..  2 / (exp(2 * x66) + 1) + x17 =E= 1;
e14..  2 / (exp(2 * x67) + 1) + x18 =E= 1;
e15..  2 / (exp(2 * x68) + 1) + x19 =E= 1;
e16..  2 / (exp(2 * x69) + 1) + x20 =E= 1;
e17..  2 / (exp(2 * x70) + 1) + x21 =E= 1;
e18..  2 / (exp(2 * x71) + 1) + x22 =E= 1;
e19..  2 / (exp(2 * x72) + 1) + x23 =E= 1;
e20..  2 / (exp(2 * x73) + 1) + x24 =E= 1;
e21..  2 / (exp(2 * x74) + 1) + x25 =E= 1;
e22..  2 / (exp(2 * x75) + 1) + x26 =E= 1;
e23..  2 / (exp(2 * x76) + 1) + x27 =E= 1;
e24..  2 / (exp(2 * x77) + 1) + x28 =E= 1;
e25..  2 / (exp(2 * x78) + 1) + x29 =E= 1;
e26..  2 / (exp(2 * x79) + 1) + x30 =E= 1;
e27..  2 / (exp(2 * x80) + 1) + x31 =E= 1;
e28..  2 / (exp(2 * x81) + 1) + x32 =E= 1;
e29..  2 / (exp(2 * x82) + 1) + x33 =E= 1;
e30..  2 / (exp(2 * x83) + 1) + x34 =E= 1;
e31..  2 / (exp(2 * x84) + 1) + x35 =E= 1;
e32..  2 / (exp(2 * x85) + 1) + x36 =E= 1;
e33..  2 / (exp(2 * x86) + 1) + x37 =E= 1;
e34..  2 / (exp(2 * x87) + 1) + x38 =E= 1;
e35..  2 / (exp(2 * x88) + 1) + x39 =E= 1;
e36..  2 / (exp(2 * x89) + 1) + x40 =E= 1;
e37..  2 / (exp(2 * x90) + 1) + x41 =E= 1;
e38..  2 / (exp(2 * x91) + 1) + x42 =E= 1;
e39..  2 / (exp(2 * x92) + 1) + x43 =E= 1;
e40..  2 / (exp(2 * x93) + 1) + x44 =E= 1;
e41..  2 / (exp(2 * x94) + 1) + x45 =E= 1;
e42..  2 / (exp(2 * x95) + 1) + x46 =E= 1;
e43..  2 / (exp(2 * x96) + 1) + x47 =E= 1;
e44..  2 / (exp(2 * x97) + 1) + x48 =E= 1;
e45..  2 / (exp(2 * x98) + 1) + x49 =E= 1;
e46..  2 / (exp(2 * x99) + 1) + x50 =E= 1;
e47..  2 / (exp(2 * x100) + 1) + x51 =E= 1;
e48..  2 / (exp(2 * x101) + 1) + x52 =E= 1;
e49..  0.065704 * x6 - 0.033719 * x7 + 0.76133 * x8 - 0.48805 * x9 + 0.10716 *
       x10 - 0.12256 * x11 - 0.47773 * x12 - 1.4593 * x13 - 0.12829 * x14 -
       0.17066 * x15 + 0.031784 * x16 - 1.0343 * x17 + 0.7515 * x18 - 0.17572 *
       x19 - 0.89455 * x20 + 1.0327 * x21 - 0.053874 * x22 - 0.32397 * x23 -
       1.8663 * x24 - 0.5493 * x25 + 0.60609 * x26 - 0.40068 * x27 + 0.92391 *
       x28 + 0.93709 * x29 + 0.24686 * x30 + 1.7127 * x31 + 0.30011 * x32 +
       0.28025 * x33 + 0.23534 * x34 - 1.205 * x35 + 0.50945 * x36 + 0.20317 *
       x37 - 0.26555 * x38 + 1.6129 * x39 + 0.28066 * x40 + 0.080875 * x41 +
       0.26354 * x42 - 0.17364 * x43 + 0.58227 * x44 + 0.15634 * x45 - 0.20363
       * x46 - 0.041905 * x47 + 0.43558 * x48 - 0.031562 * x49 + 1.0758 * x50
       + 0.96224 * x51 - 0.042862 * x52 + x54 =E= -0.060465315174905;
e50..  x53 - 6.969979437085875 * x54 =E= 0.7601908525553558;
e51..  -0.33393267662969284 * x2 + x4 =E= -0.0004457779206294976;
e52..  -0.3345887696749378 * x3 + x5 =E= -0.0002029955280284934;
e53..  -9.10703116886844 * x4 - 2.94337038212874 * x5 + x55 =E=
       -9.63015944232877;
e54..  6.93102790414726 * x4 - 3.75196310820969 * x5 + x56 =E=
       7.31017275430626;
e55..  3.36432203670221 * x4 + 0.82525521613015 * x5 + x57 =E=
       2.98200536306973;
e56..  1.64194568809983 * x4 + 4.48523835606202 * x5 + x58 =E=
       2.77237105961281;
e57..  -0.00226437988375905 * x4 + 4.867765277275 * x5 + x59 =E=
       -4.42497349082323;
e58..  7.19863262227284 * x4 + 1.87895940079179 * x5 + x60 =E=
       6.25777205138423;
e59..  -0.74811043850941 * x4 + 4.20191684807602 * x5 + x61 =E=
       -2.62626886981211;
e60..  2.65321880831968 * x4 + 2.19715149631687 * x5 + x62 =E=
       1.60241051102647;
e61..  1.95895703624561 * x4 + 6.61501085095858 * x5 + x63 =E=
       -3.21372438941966;
e62..  0.976462786697995 * x4 + 5.4722226686442 * x5 + x64 =E=
       -3.43511278570442;
e63..  9.05631954225151 * x4 - 0.860748840616473 * x5 + x65 =E=
       6.80778429540444;
e64..  2.51698650443046 * x4 - 1.12325188704783 * x5 + x66 =E=
       1.46066391523409;
e65..  2.53263349216247 * x4 - 2.83124829526224 * x5 + x67 =E=
       2.00914786562159;
e66..  1.64022926216511 * x4 - 6.71323991116741 * x5 + x68 =E=
       2.30586986684063;
e67..  1.7873770187918 * x4 - 3.68278580116741 * x5 + x69 =E= 1.39928381929576;
e68..  4.22195373550896 * x4 - 0.396477134417836 * x5 + x70 =E=
       0.964209592889774;
e69..  2.41239470358791 * x4 - 8.80924154690345 * x5 + x71 =E=
       4.23134871494298;
e70..  -0.442923139035927 * x4 - 5.28020902797231 * x5 + x72 =E=
       2.04241734851624;
e71..  3.51805314742391 * x4 - 1.30278510763279 * x5 + x73 =E=
       0.0651561391008471;
e72..  -0.113212023605603 * x4 + 4.72324347930784 * x5 + x74 =E=
       -0.853205151783354;
e73..  3.95665396270945 * x4 + 1.27626711582506 * x5 + x75 =E=
       0.814440074164862;
e74..  4.7695955444504 * x4 + 0.773487861729487 * x5 + x76 =E=
       -0.111247602721831;
e75..  2.05027781679787 * x4 - 2.50975207869453 * x5 + x77 =E=
       0.0820486511860433;
e76..  3.66654493886071 * x4 + 2.38892762517696 * x5 + x78 =E=
       -0.891390460987188;
e77..  3.27998735486886 * x4 - 2.59050296919374 * x5 + x79 =E=
       -0.739390789012633;
e78..  1.6153208627896 * x4 + 2.33417975474504 * x5 + x80 =E=
       0.871854475217263;
e79..  -1.11358422125162 * x4 - 5.30599002390186 * x5 + x81 =E=
       -1.00704834952813;
e80..  -2.92402686265607 * x4 - 2.89613202071523 * x5 + x82 =E=
       -0.232468557606477;
e81..  -1.81867167443697 * x4 + 7.33812407332642 * x5 + x83 =E=
       2.54135224708381;
e82..  3.10542197925959 * x4 + 2.12619668948654 * x5 + x84 =E=
       -0.68717003462119;
e83..  1.74472150970003 * x4 + 4.95282077029394 * x5 + x85 =E=
       -2.17551955892824;
e84..  -2.65152859120729 * x4 + 4.38271460759243 * x5 + x86 =E=
       1.53042126339426;
e85..  4.1487314966423 * x4 + 1.36838462771498 * x5 + x87 =E=
       -2.02423652126007;
e86..  3.71026588633397 * x4 - 0.240322230905286 * x5 + x88 =E=
       -0.902116571066426;
e87..  0.136858569888465 * x4 + 6.22839150715604 * x5 + x89 =E=
       2.22245776134561;
e88..  -2.29273626384379 * x4 + 9.49277618264744 * x5 + x90 =E=
       4.61447478864626;
e89..  -3.29404103074185 * x4 - 4.22870341832834 * x5 + x91 =E=
       2.65015883530254;
e90..  0.236622607550426 * x4 + 6.32282202964636 * x5 + x92 =E=
       4.10022407859802;
e91..  -3.50739896377168 * x4 + 1.52421925481854 * x5 + x93 =E=
       1.81299728715722;
e92..  -3.82419999460229 * x4 + 3.12341880053042 * x5 + x94 =E=
       3.64656884309529;
e93..  -3.66913363409212 * x4 + 0.319990400846123 * x5 + x95 =E=
       2.89624962044085;
e94..  -8.1823967031854 * x4 - 4.01934818658146 * x5 + x96 =E=
       7.19040411962699;
e95..  2.45448375388046 * x4 - 4.00420657536838 * x5 + x97 =E=
       -2.8116643770919;
e96..  6.4400062979969 * x4 + 8.07408273005427 * x5 + x98 =E=
       -6.51730187495992;
e97..  -4.28496179289514 * x4 + 8.05160576591809 * x5 + x99 =E=
       9.22764002248408;
e98..  4.52908595891183 * x4 - 8.45807037184382 * x5 + x100 =E=
       -9.71433325733342;
e99..  9.03003295779029 * x4 + 5.87007164848379 * x5 + x101 =E=
       -8.54369465648149;

* set non-default bounds
x2.lo = -3; x2.up = 3;
x3.lo = -3; x3.up = 3;

Model m / all /;

m.limrow = 0;
m.tolproj=0.0;
m.limcol = 0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;


Last updated: 2022-06-23 Git hash: c4ba8ecd
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