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About

Pure implementation of Gradient Descent With Line Search and Newton Optimization algorithms in Python.

Requirements

  • Numpy

  • Sympy

pip install numpy
pip install sympy

How to run

Clone the project in a arbitrary directory, run main.py.

Important tips

  • Use Python operators inside your arbitrary function, for example use: a**b for power NOT a^b.
  • If you use mathematics functions inside your arbitrary function use Python math lib functions, for example use: exp(y) for exponential or acosh(), tan() etc for trigonometric functions.
  • If your arbitrary function contains functions like exp or sin DO NOT USE variables with names: e, x, p, s, i, n. In simpler term DO NOT define exp(x) or sin(s) , Instead define: exp(a) or sin(x).

Some example of valid functions:

(x - 4)**4 - (y - 3)**2 + (sin(z*x) * tanh(y**2.7182)) - 4*(z + 5)**4

0.3454663*y**2 + 30*x*y + 21.69*x**2 - 293.074*y

x**3 - 12*x*y + 8*y**3

atan(sinh(x**2 - 2*y))

1000*x**2 + 40*x*y + y**2

exp(a-b) + exp(b-a) + exp(a**2) + c**2

x**2 + 2*(y)**2

log(x) - (x - 4)**4 + -1*log(1 - x - y + x*y*z) + - 0.3454663*y**2 + (y - 3)**2 + (sin(z*x) * tanh(y**2.7182)) + 30*x*y - 4*(z + 5)**4 + log(y) + 21.69*x**2 - 293.074*y

-1*(x**3 - y**2) + 1.4142

-1*log(x**3 + x**2 - 5*x + 6)

x**3 - 6*x**2 + 4*x + 12

x**(1/x)

exp(a-b) + exp(b-a)

40.0708*x*y + 592.56*x**2 + 0.01*y**2 - 85.863*x

x**4 - 4*x*y + y**4

-1*log(1 - x - y) - log(x) - log(y)

sqrt(1 + x**2)

7*x - log(x)

-1*(x**2 + y**2) + 4

100*x**4 + 0.01*y**4

(1 - x)**2 + 100*(y - x**2)**2

sin(0.5*a**2 - 0.25*b**2 + 3) * cos(2*a + 1 - exp(b))

100*(y - x**2)**2 + (1 - x)**2

-1*(x**3 - y**2) + 1.4142

-1*log(x**3 + x**2 - 5*x + 6)

x**3 - 6*x**2 + 4*x + 12

x**(1/x)

sin(x) / x