In an unconstrained two-variable problem with a quadratic objective function, there will always be a local optimal solution, though global optimal solution may not be available even in such problems.

Question

Quizplus · Accepted Answer

In an unconstrained two-variable problem with a quadratic objective function, if the function is convex (or concave), there will always be a global optimal solution, not just a local one, because a quadratic function is either always convex or always concave, leading to a unique extremum.

In an Unconstrained Two-Variable Problem with a Quadratic Objective Function