Constrained optimization local numerical introduction

Tutorial 3 steps, run in order in one session. Every step was executed against the engine and the output below is what it produced.

Step 1

Minimize[{x - y, -3 x^2 + 2 x y - y^2 ≥ -1}, {x, y}]

Output

Minimize[{x - y, -3*x^2 + 2*x*y - y^2 >= -1}, {x, y}]

Step 2

NMinimize[{x - y, -3 x^2 + 2 x y - y^2 ≥ -1}, {x, y}]

Output

{-0.9999999999999983, {x -> -2.6829876645246468*^-8, y -> 0.9999999731701217}}

Step 3

FindMinimum[{x - y, -3 x^2 + 2 x y - y^2 ≥ -1}, {x, y}]

Output

{-0.9999999999999983, {x -> -2.6829876645246468*^-8, y -> 0.9999999731701217}}

Functions used