Epäkonvekseina

Epäkonvekseina is a Finnish term that translates to "non-convex" in English, primarily used in geometry and optimization. In the context of geometry, a set or shape is considered non-convex if there exists at least one pair of points within the set such that the line segment connecting these two points lies partially or entirely outside the set. Convex shapes, in contrast, have the property that every line segment connecting any two points within the shape is entirely contained within the shape. Examples of non-convex shapes include star shapes, crescent moons, or any shape with indentations or holes.

In mathematical optimization, a function is considered non-convex if its feasible region (the set of points where the function is defined and constraints are met) or its objective function itself is non-convex. Optimization problems involving non-convex functions are generally much harder to solve than their convex counterparts. This is because non-convex problems can have multiple local optima, and algorithms designed to find the global optimum may get trapped in a local optimum. Finding the true global minimum or maximum in a non-convex optimization problem often requires more sophisticated algorithms or exhaustive search methods. The study and handling of non-convexity are crucial in fields such as engineering, economics, and computer science where optimization plays a significant role.