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PDE-constrained optimization is a subset of mathematical optimization where at least one of the constraints may be expressed as a partial differential equation. [1] Typical domains where these problems arise include aerodynamics , computational fluid dynamics , image segmentation , and inverse problems . [ 2 ]
A particle swarm searching for the global minimum of a function. In computational science, particle swarm optimization (PSO) [1] is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality.
The concept of fuzzy stability is considered as an extension into a time interval, taking into account the corresponding stability area of the decision maker. The more complex is the model, the softer a choice has to be considered. The idea of fuzzy equilibrium is based on the optimization principles.
This breaks a dynamic optimization problem into a sequence of simpler subproblems, as Bellman's “principle of optimality" prescribes. [3] The equation applies to algebraic structures with a total ordering; for algebraic structures with a partial ordering, the generic Bellman's equation can be used. [4]
It can be thought of as the rate of change of the function in the -direction.. Sometimes, for = (,, …), the partial derivative of with respect to is denoted as . Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in:
In complex analysis of one and several complex variables, Wirtinger derivatives (sometimes also called Wirtinger operators [1]), named after Wilhelm Wirtinger who introduced them in 1927 in the course of his studies on the theory of functions of several complex variables, are partial differential operators of the first order which behave in a very similar manner to the ordinary derivatives ...
Vector optimization is a subarea of mathematical optimization where optimization problems with a vector-valued objective functions are optimized with respect to a given partial ordering and subject to certain constraints.
Partial least squares (PLS) regression is a statistical method that bears some relation to principal components regression and is a reduced rank regression; [1] instead of finding hyperplanes of maximum variance between the response and independent variables, it finds a linear regression model by projecting the predicted variables and the observable variables to a new space of maximum ...