Search results
Results From The WOW.Com Content Network
For example, x ∗ is a strict global maximum point if for all x in X with x ≠ x ∗, we have f(x ∗) > f(x), and x ∗ is a strict local maximum point if there exists some ε > 0 such that, for all x in X within distance ε of x ∗ with x ≠ x ∗, we have f(x ∗) > f(x). Note that a point is a strict global maximum point if and only if ...
Many of these energy minimization problems can be approximated by solving a maximum flow problem in a graph [2] (and thus, by the max-flow min-cut theorem, define a minimal cut of the graph). Under most formulations of such problems in computer vision, the minimum energy solution corresponds to the maximum a posteriori estimate of a solution.
MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
As a simple example, consider the problem of finding the value of x that minimizes = , constrained such that = . (This problem is somewhat untypical because there are only two values that satisfy this constraint, but it is useful for illustration purposes because the corresponding unconstrained function can be visualized in three dimensions.)
The examples 1 and 2 denote different terms, differing only in where the parentheses are placed. They have different meanings: example 1 is a function definition, while example 2 is a function application. The lambda variable x is a placeholder in both examples. Here, example 1 defines a function .
The canonical optimization variant of the above decision problem is usually known as the Maximum-Cut Problem or Max-Cut and is defined as: Given a graph G, find a maximum cut. The optimization variant is known to be NP-Hard. The opposite problem, that of finding a minimum cut is known to be efficiently solvable via the Ford–Fulkerson algorithm.
If f(n) = n 2 + 3n, then as n becomes very large, the term 3n becomes insignificant compared to n 2. The function f(n) is said to be "asymptotically equivalent to n 2, as n → ∞". This is often written symbolically as f (n) ~ n 2, which is read as "f(n) is asymptotic to n 2". An example of an important asymptotic result is the prime number ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.