<p>Minimizer</p>

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<p>Minimizer</p>

AUXILIARY FUNCTIONS

Limits output in the interval [L1,L2]: x L1 L2 limit x L1 ≤ out L1 : x L2 ≥ out L2 : out x : if if out 21 line :

Passes only positive values: x diode x x 0 > (* :

1 J x x.m x.M NumIt 1 g A b dt α λ minimize y x g : z A x * b - : n x rows : m y rows : r z rows : k 1 NumIt range w A transpose z * eval : ξ b A x * - eval : L 1 n range x.unLim x L el α x J x L el diff x g j el x L el diff y j el * (j 1 m sum - w L el - (* - eval : x L el x L el λ dt * x.unLim x.m L el x.M L el limit x L el - (* + eval : 21 line for L 1 m range y.unLim y L el x g L el - eval : y L el y L el λ dt * y.unLim diode y L el - (* + eval : 21 line for L 1 r range z L el z L el λ dt * ξ L el * + eval : for 51 line for x x J x g A x * b - 41 sys 71 line :

Ref.:Mohsen Alipour, Davood Rostamy, Alaeddin Malek: "A Recurrent Neural Network for Nonlinear Convex Optimization with Application to a Class of Variational Inequalities Problems"

EXAMPLE 1 of the reference

INPUTS

x J1 14 / x 1 el 4^* 0.5 x 1 el 2^* + 14 / x 2 el 4^* + 0.5 x 2 el 2^* + 0.9 x 1 el * x 2 el * - :

function to be minimized

x 33 - 21 mat :

initial value (guess)

x.m 0021 mat :

x.M 1121 mat :

minimum and maximum values

x g1 x 1 el - x 2 el - 2 + x 1 el x 2 el - 2 + x 1 el 2^- x 2 el - 3 + 31 mat :

inequality constraint: g(x)>=0 (can be nonlinear)

A 13 - 12 mat :

b 2 - :

linear equality constraint: A*x + b = 0

λ 1 :

α 1 :

dt 0.1 :

NumIt 300 :

s J1 x x.m x.M NumIt s g1 A b dt α λ minimize 0.3461 0.782 21 mat 0.2192 0.8719 1.5641 2.0982 31 mat 1.179 1012 -^* - 41 sys

the value of the minimum

the value of the function in the minimum

the nonlinear positive constraints of the function in the minimum

the linear equality constraints (should be 0)

EXAMPLE 2 of the referance

INPUTS

x J2 0.4 x 1 el * x 1 el 2^+ x 2 el 2^+ x 1 el x 2 el * - 0.5 x 3 el 2^* + 0.5 x 4 el 2^* + x 1 el 3^30 / + :

function to be minimized

x 0.1 0 0.5 341 mat :

initial value (guess)

x.m 000041 mat :

x.M 10010010010041 mat :

minimum and maximum values

x g2 0.5 x 1 el * - x 2 el - x 4 el + 0.5 + 3 x 1 el * - x 1 el x 2 el * + 1 + 21 mat :

inequality constraints: g(x)>=0 (can be nonlinear)

A 1 0.5 1 - 014 mat :

b 0.4 :

linear equality constraints: A*x + b = 0

λ 1 :

α 1 :

dt 0.1 :

NumIt 300 :

s J2 x x.m x.M NumIt s g2 A b dt α λ minimize 0.2567 0.2867 2.2 1014 -^* 3.286 1012 -^* 41 mat 0.1777 0.085 0.3036 21 mat 2.0321 108 -^* 41 sys

the value of the minimum

the value of the function in the minimum

the nonlinear positive constraints of the function in the minimum

the linear equality constraints (should be 0)

The same function as above, but with different initial conditions:

s J2 5 - 15 0.5 441 mat x.m x.M NumIt s g2 A b dt α λ minimize 0.2567 0.2867 9.501 1012 -^* 1.1017 107 -^* 41 mat 0.1777 0.085 0.3035 21 mat 2.2314 105 -^* 41 sys

the value of the minimum

the value of the function in the minimum

the nonlinear positive constraints of the function in the minimum

the linear equality constraints (should be 0)