Search results
Results From The WOW.Com Content Network
GPOPS-II [3] is designed to solve multiple-phase optimal control problems of the following mathematical form (where is the number of phases): = ((), …, ()) subject to the dynamic constraints
The image of a function f(x 1, x 2, …, x n) is the set of all values of f when the n-tuple (x 1, x 2, …, x n) runs in the whole domain of f.For a continuous (see below for a definition) real-valued function which has a connected domain, the image is either an interval or a single value.
The rectangular region at the bottom of the body is the domain of integration, while the surface is the graph of the two-variable function to be integrated. In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z).
A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends upon the material of the medium. One corresponding concept in mechanics is the principle of least/stationary action. Many important problems involve functions of several variables.
Plot of the Rosenbrock function of two variables. Here a = 1 , b = 100 {\displaystyle a=1,b=100} , and the minimum value of zero is at ( 1 , 1 ) {\displaystyle (1,1)} . In mathematical optimization , the Rosenbrock function is a non- convex function , introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for ...
The two critical points occur at saddle points where x = 1 and x = −1. In order to solve this problem with a numerical optimization technique, we must first transform this problem such that the critical points occur at local minima. This is done by computing the magnitude of the gradient of the unconstrained optimization problem.
For very simple problems, say a function of two variables subject to a single equality constraint, it is most practical to apply the method of substitution. [4] The idea is to substitute the constraint into the objective function to create a composite function that incorporates the effect of the constraint.
Holomorphic functions of several complex variables satisfy an identity theorem, as in one variable : two holomorphic functions defined on the same connected open set and which coincide on an open subset N of D, are equal on the whole open set D. This result can be proven from the fact that holomorphics functions have power series extensions ...