Math Problem Statement

No lineal por gradiente Considere el siguiente problema de optimización no restringida:

Maximizar: f(x) = 2x1x2 + x2 - x12 - 2x22 o bien

              f(x) = 2x1x2 - 2x12 - x22

puede escoger cualquiera de las dos.

Comenzando con la solución prueba inicial (x1, x2) = (1, 1)

Solution

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Math Problem Analysis

Mathematical Concepts

Optimization
Unconstrained Optimization
Gradient Method

Formulas

f(x) = 2x1x2 + x2 - x12 - 2x22
f(x) = 2x1x2 - 2x12 - x22
∇f(x) = (∂f/∂x1, ∂f/∂x2)
x_k = x_{k-1} - α ∇f(x_{k-1})

Theorems

Gradient Descent Method

Suitable Grade Level

Undergraduate