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Armadillo is a C++ linear algebra library (matrix and vector maths), aiming towards a good balance between speed and ease of use. [1] It employs template classes, and has optional links to BLAS and LAPACK. The syntax is similar to MATLAB. Blitz++ is a high-performance vector mathematics library written in C++.
Interior point methods: This is a large class of methods for constrained optimization, some of which use only (sub)gradient information and others of which require the evaluation of Hessians. Methods that evaluate gradients, or approximate gradients in some way (or even subgradients):
Theoretical analysis indicates that some optimization problems are NP-complete, or even undecidable. [2] Also, producing perfectly optimal code is not possible since optimizing for one aspect often degrades performance for another. Optimization is a collection of heuristic methods for improving resource usage in typical programs. [3]: 585
Constraint programming (CP) [1] is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state the constraints on the feasible solutions for a set of decision variables.
Stochastic optimization (SO) are optimization methods that generate and use random variables. For stochastic optimization problems, the objective functions or constraints are random. Stochastic optimization also include methods with random iterates .
The conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. It is commonly attributed to Magnus Hestenes and Eduard Stiefel, [1] [2] who programmed it on the Z4, [3] and extensively researched it. [4] [5] The biconjugate gradient method provides a generalization to non-symmetric matrices.
Blitz++ is a C++ template class library that provides high-performance multidimensional array containers for scientific computing. Boost uBLAS J. Walter, M. Koch C++ 2000 1.84.0 / 12.2023 Free Boost Software License uBLAS is a C++ template class library that provides BLAS level 1, 2, 3 functionality for dense, packed and sparse matrices. Dlib
Powell's method, strictly Powell's conjugate direction method, is an algorithm proposed by Michael J. D. Powell for finding a local minimum of a function. The function need not be differentiable, and no derivatives are taken. The function must be a real-valued function of a fixed number of real-valued inputs.