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The problem to determine all positive integers such that the concatenation of and in base uses at most distinct characters for and fixed [citation needed] and many other problems in the coding theory are also the unsolved problems in mathematics.
Packing circles in a square - closely related to spreading points in a unit square with the objective of finding the greatest minimal separation, d n, between points. To convert between these two formulations of the problem, the square side for unit circles will be L = 2 + 2 / d n {\displaystyle L=2+2/d_{n}} .
MOSEK is a commercial solver capable of solving geometric programs as well as other non-linear optimization problems. CVXOPT is an open-source solver for convex optimization problems. GPkit is a Python package for cleanly defining and manipulating geometric programming models. There are a number of example GP models written with this package here.
The problem of covering a polygon with star polygons is a variant of the art gallery problem. The visibility graph for the problem of minimally covering hole-free rectilinear polygons with star polygons is a perfect graph. This perfectness property implies a polynomial algorithm for finding a minimum covering of any rectilinear polygon with ...
Written in C++ and published under an MIT license, HiGHS provides programming interfaces to C, Python, Julia, Rust, R, JavaScript, Fortran, and C#. It has no external dependencies. A convenient thin wrapper to Python is available via the highspy PyPI package. Although generally single-threaded, some solver components can utilize multi-core ...
C mathematical operations are a group of functions in the standard library of the C programming language implementing basic mathematical functions. [1] [2] All functions use floating-point numbers in one manner or another. Different C standards provide different, albeit backwards-compatible, sets of functions.
An illustration of Monte Carlo integration. In this example, the domain D is the inner circle and the domain E is the square. Because the square's area (4) can be easily calculated, the area of the circle (π*1.0 2) can be estimated by the ratio (0.8) of the points inside the circle (40) to the total number of points (50), yielding an approximation for the circle's area of 4*0.8 = 3.2 ≈ π.
A sum-of-squares optimization program is an optimization problem with a linear cost function and a particular type of constraint on the decision variables. These constraints are of the form that when the decision variables are used as coefficients in certain polynomials, those polynomials should have the polynomial SOS property.