Search results
Results From The WOW.Com Content Network
GPE is a model equation for the ground-state single-particle wavefunction in a Bose–Einstein condensate. It is similar in form to the Ginzburg–Landau equation and is sometimes referred to as the " nonlinear Schrödinger equation ". The non-linearity of the Gross–Pitaevskii equation has its origin in the interaction between the particles ...
Website. www.highs.dev. HiGHS is open-source software to solve linear programming (LP), mixed-integer programming (MIP), and convex quadratic programming (QP) models. [1] Written in C++ and published under an MIT license, HiGHS provides programming interfaces to C, Python, Julia, Rust, JavaScript, Fortran, and C#. It has no external dependencies.
Given a transformation between input and output values, described by a mathematical function, optimization deals with generating and selecting the best solution from some set of available alternatives, by systematically choosing input values from within an allowed set, computing the output of the function and recording the best output values found during the process.
Cnoidal wave solution to the Korteweg–De Vries equation, in terms of the square of the Jacobi elliptic function cn (and with value of the parameter m = 0.9). Numerical solution of the KdV equation u t + uu x + δ 2 u xxx = 0 (δ = 0.022) with an initial condition u(x, 0) = cos(πx). Time evolution was done by the Zabusky–Kruskal scheme. [1]
The term "Bellman equation" usually refers to the dynamic programming equation (DPE) associated with discrete-time optimization problems. [5] In continuous-time optimization problems, the analogous equation is a partial differential equation that is called the Hamilton–Jacobi–Bellman equation. [6][7] In discrete time any multi-stage ...
Pseudo-spectral method. Pseudo-spectral methods, [1] also known as discrete variable representation (DVR) methods, are a class of numerical methods used in applied mathematics and scientific computing for the solution of partial differential equations. They are closely related to spectral methods, but complement the basis by an additional ...
Relaxation (iterative method) In numerical mathematics, relaxation methods are iterative methods for solving systems of equations, including nonlinear systems. [1] Relaxation methods were developed for solving large sparse linear systems, which arose as finite-difference discretizations of differential equations. [2][3] They are also used for ...
Geometric programming is closely related to convex optimization: any GP can be made convex by means of a change of variables. [2] GPs have numerous applications, including component sizing in IC design, [3][4] aircraft design, [5] maximum likelihood estimation for logistic regression in statistics, and parameter tuning of positive linear ...