Konveksioptimointi
Konveksioptimointi, also known as convex optimization, is a subfield of mathematical optimization that deals with the minimization or maximization of convex functions. Convex optimization problems are characterized by their convex objective functions and convex constraint sets, which ensure that any local minimum is also a global minimum. This property makes convex optimization problems easier to solve compared to general non-convex problems.
The standard form of a convex optimization problem can be written as:
subject to g_i(x) ≤ 0, i = 1, ..., m
where f is a convex function, g_i are convex inequality constraints, and h_j are affine equality constraints.
Convex optimization has wide-ranging applications in various fields, including engineering, economics, machine learning, and signal processing.
One of the key advantages of convex optimization is its computational efficiency. Many convex optimization problems
However, not all optimization problems are convex. In practice, many real-world problems involve non-convex functions and