What is a pseudoconvex domain?
What is a pseudoconvex domain?
for all real numbers. In other words, a domain is pseudoconvex if. has a continuous plurisubharmonic exhaustion function. Every (geometrically) convex set is pseudoconvex. However, there are pseudoconvex domains which are not geometrically convex.
What is CR math?
The name itself has two etymologies: CR stands for Cauchy-Riemann and suggests the Cauchy-Riemann equations; CR also stands for complex-real and suggests real submanifolds of complex spaces.
How do you prove a function is Pseudoconvex?
We prove that a function, defined on some interval, is pseudoconvex if and only if its domain can be split into three parts such that the function is strictly monotone decreasing in the first part, constant in the second one, strictly monotone increasing in the third part, and every stationary point is a global …
What is pseudo concave?
In convex analysis and the calculus of variations, both branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minima, but need not actually be convex. The property must hold in all of the function domain, and not only for nearby points.
What does CR mean in calculus?
The subbundle L is called a CR structure on the manifold M. The abbreviation CR stands for “Cauchy–Riemann” or “Complex-Real”.
What does Pseudolinear mean?
A pseudolinear function is a function that is both pseudoconvex and pseudoconcave. For example, linear–fractional programs have pseudolinear objective functions and linear–inequality constraints. These properties allow fractional-linear problems to be solved by a variant of the simplex algorithm (of George B. Dantzig).
How do you prove a function is pseudoconvex?
What does CR mean electrical?
The letters often represent the type of device, such as M for motor starter or CR for control relay.
What is a pseudoconvex function?
In convex analysis and the calculus of variations, both branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minima, but need not actually be convex.
What is the difference between pseudoconcave and pseudolinear?
A pseudoconcave function is a function whose negative is pseudoconvex. A pseudolinear function is a function that is both pseudoconvex and pseudoconcave. For example, linear–fractional programs have pseudolinear objective functions and linear–inequality constraints.
What is the converse of every convex function?
Every convex function is pseudoconvex, but the converse is not true. For example, the function is pseudoconvex but not convex. Similarly, any pseudoconvex function is quasiconvex; but the converse is not true, since the function is quasiconvex but not pseudoconvex. This can be summarized schematically as:
