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Extended Mathematical Programming (EMP) is an extension to mathematical programming languages that provides several keywords for bilevel optimization problems. These annotations facilitate the automatic reformulation to Mathematical Programs with Equilibrium Constraints (MPECs) for which mature solver technology exists.
Python's Guido van Rossum summarizes C3 superclass linearization thus: [11] Basically, the idea behind C3 is that if you write down all of the ordering rules imposed by inheritance relationships in a complex class hierarchy, the algorithm will determine a monotonic ordering of the classes that satisfies all of them.
Clearly, a #P problem must be at least as hard as the corresponding NP problem, since a count of solutions immediately tells if at least one solution exists, if the count is greater than zero. Surprisingly, some #P problems that are believed to be difficult correspond to easy (for example linear-time) P problems. [18]
The parameters of the LNP model consist of the linear filters {} and the nonlinearity . The estimation problem (also known as the problem of neural characterization) is the problem of determining these parameters from data consisting of a time-varying stimulus and the set of observed spike times. Techniques for estimating the LNP model ...
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 ...
A linear programming problem is one in which we wish to maximize or minimize a linear objective function of real variables over a polytope.In semidefinite programming, we instead use real-valued vectors and are allowed to take the dot product of vectors; nonnegativity constraints on real variables in LP (linear programming) are replaced by semidefiniteness constraints on matrix variables in ...
The smallest circle problem can be generalized to the smallest ball enclosing a set of balls, [3] to the smallest ball that touches or surrounds each of a set of balls, [4] to the weighted 1-center problem, [5] or to similar smaller enclosing ball problems in non-Euclidean spaces such as the space with distances defined by Bregman divergence. [6]
SOCPs can be solved by interior point methods [2] and in general, can be solved more efficiently than semidefinite programming (SDP) problems. [3] Some engineering applications of SOCP include filter design, antenna array weight design, truss design, and grasping force optimization in robotics. [4]