Let's consider a following method for minimization function f on a square Q. One solves task of minimization for a function f on a horizontal segment in a square's center with an accuracy delta (may be on function). After that one calculates a (sub-)gradient in a received point and chooses the rectangle which the (sub-)gradient "does not look" in. Similar actions are repeated for a vertical segment. As a result we have the square decreased twice. It was the first iteration. Following iterations are performed for a new squares similarly.
Let's find cases when method works correctly. Also let's find a possible value of error delta for task on segment and a sufficient iteration's number N to solve the initial task with accuracy epsilon on function.
-
Theoretical results: it is results and their proofs. There are estimate of delta and N, some facts about efficiency and tests results here.
-
Tests: there are a code for the method, test's functions and a brief description of their properties here.
-
Tests results in .ipynb is the code and tests' results