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APMonitor
Advanced process monitor (APMonitor) is a modeling language for differential algebraic ( DAE) equations. It is a free web-service or local server for solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and solves linear programming, integer programming, nonlinear programming, nonlinear mixed integer programming, dynamic simulation, moving horizon estimation, and nonlinear model predictive control. APMonitor does not solve the problems directly, but calls nonlinear programming solvers such as APOPT, BPOPT, IPOPT, MINOS, and SNOPT. The APMonitor API provides exact first and second derivatives of continuous functions to the solvers through automatic differentiation and in sparse matrix form. Programming language integration Julia, MATLAB, Python are mathematical programming languages that have APMonitor integration through web-service APIs. The GEKKO Optimization Suite is a recent extension of APMonitor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
APMonitor Trend
Advanced process monitor (APMonitor) is a modeling language for differential algebraic ( DAE) equations. It is a free web-service or local server for solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and solves linear programming, integer programming, nonlinear programming, nonlinear mixed integer programming, dynamic simulation, moving horizon estimation, and nonlinear model predictive control. APMonitor does not solve the problems directly, but calls nonlinear programming solvers such as APOPT, BPOPT, IPOPT, MINOS, and SNOPT. The APMonitor API provides exact first and second derivatives of continuous functions to the solvers through automatic differentiation and in sparse matrix form. Programming language integration Julia, MATLAB, Python are mathematical programming languages that have APMonitor integration through web-service APIs. The GEKKO Optimization Suite is a recent extension of APMonit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gekko (optimization Software)
The GEKKO Python package solves large-scale mixed-integer and differential algebraic equations with nonlinear programming solvers (IPOPT, APOPT, BPOPT, SNOPT, MINOS). Modes of operation include machine learning, data reconciliation, real-time optimization, dynamic simulation, and nonlinear model predictive control. In addition, the package solves Linear programming (LP), Quadratic programming (QP), Quadratically constrained quadratic program (QCQP), Nonlinear programming (NLP), Mixed integer programming (MIP), and Mixed integer linear programming (MILP). GEKKO is available in Python and installed with pip from PyPI of the Python Software Foundation. pip install gekko GEKKO works on all platforms and with Python 2.7 and 3+. By default, the problem is sent to a public server where the solution is computed and returned to Python. There are Windows, MacOS, Linux, and ARM (Raspberry Pi) processor options to solve without an Internet connection. GEKKO is an extension of the A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Numerical Analysis Software
Listed here are notable end-user computer applications intended for use with numerical or data analysis: Numerical-software packages General-purpose computer algebra systems Interface-oriented Language-oriented Historically significant * Expensive Desk Calculator written for the TX-0 The TX-0, for ''Transistorized Experimental computer zero'', but affectionately referred to as tixo (pronounced "tix oh"), was an early fully transistorized computer and contained a then-huge 64 K of 18-bit words of magnetic-core memory. Const ... and PDP-1 in the late 1950s or early 1960s. * S is an (array-based) programming language with strong numerical support. R is an implementation of the S language. See also References {{DEFAULTSORT:Numerical Analysis Software Lists of software Mathematics-related lists *Software ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
APOPT
APOPT (for Advanced Process OPTimizer) is a software package for solving large-scale optimization problems of any of these forms: * Linear programming (LP) * Quadratic programming (QP) * Quadratically constrained quadratic program (QCQP) * Nonlinear programming (NLP) * Mixed integer programming (MIP) * Mixed integer linear programming (MILP) * Mixed integer nonlinear programming (MINLP) Applications of the APOPT include chemical reactors, friction stir welding, prevention of hydrate formation in deep-sea pipelines, computational biology, solid oxide fuel cells, and flight controls for Unmanned Aerial Vehicles (UAVs). Benchmark Testing Standard benchmarks such as CUTEr and SBML curated models are used to test the performance of APOPT relative to solvers BPOPT, IPOPT, SNOPT, and MINOS. A combination of APOPT (Active Set SQP) and BPOPT (Interior Point Method) performed the best on 494 benchmark problems for solution speed and total fraction of problems solved. See also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moving Horizon Estimation
Moving horizon estimation (MHE) is an optimization approach that uses a series of measurements observed over time, containing noise (random variations) and other inaccuracies, and produces estimates of unknown variables or parameters. Unlike deterministic approaches, MHE requires an iterative approach that relies on linear programming or nonlinear programming solvers to find a solution. MHE reduces to the Kalman filter under certain simplifying conditions. A critical evaluation of the extended Kalman filter and the MHE found that the MHE improved performance at the cost of increased computational expense. Because of the computational expense, MHE has generally been applied to systems where there are greater computational resources and moderate to slow system dynamics. However, in the literature there are some methods to accelerate this method. Overview The application of MHE is generally to estimate measured or unmeasured states of dynamical systems. Initial conditions and paramet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SNOPT
SNOPT, for Sparse Nonlinear OPTimizer, is a software package for solving large-scale nonlinear optimization problems written by Philip Gill, Walter Murray and Michael Saunders. SNOPT is mainly written in Fortran, but interfaces to C, C++, Python and MATLAB are available. It employs a sparse sequential quadratic programming (SQP) algorithm with limited-memory quasi-Newton approximations to the Hessian of the Lagrangian. It is especially effective for nonlinear problems with functions and gradients that are expensive to evaluate. The functions should be smooth but need not be convex. SNOPT is used in several trajectory optimization software packages, including Copernicus, AeroSpace Trajectory Optimization and Software ( ASTOS), General Mission Analysis Tool, and Optimal Trajectories by Implicit Simulation (OTIS). It is also available in the Astrogator module of Systems Tool Kit. SNOPT is supported in the AIMMS, AMPL, APMonitor Advanced process monitor (APMonitor) is a model ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IPOPT
IPOPT, short for "Interior Point OPTimizer, pronounced I-P-Opt", is a software library for large scale nonlinear optimization of continuous systems. It is written in Fortran and C and is released under the EPL (formerly CPL). IPOPT implements a primal-dual interior point method, and uses line searches based on Filter methods ( Fletcher and Leyffer). IPOPT can be called from various modeling environments and C. IPOPT is part of the COIN-OR project. IPOPT is designed to exploit 1st and 2nd derivative ( Hessians) information if provided (usually via automatic differentiation routines in modeling environments such as AMPL). If no Hessians are provided, IPOPT will approximate them using a quasi-Newton methods, specifically a BFGS update. IPOPT was originally developed by Ph.D. studenAndreas Wächterand ProfLorenz T. Bieglerof the Department of Chemical Engineering at Carnegie Mellon University. Their work was recognized with thINFORMS Computing Society Prizein 2009. Arv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Predictive Control
Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The main advantage of MPC is the fact that it allows the current timeslot to be optimized, while keeping future timeslots in account. This is achieved by optimizing a finite time-horizon, but only implementing the current timeslot and then optimizing again, repeatedly, thus differing from a linear–quadratic regulator ( LQR). Also MPC has the ability to anticipate future events and can take control actions accordingly. PID controllers do not have this predictive ability. MPC is nearly universally implemented a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MINOS (optimization Software)
__NOTOC__ MINOS is a Fortran software package for solving linear and nonlinear mathematical optimization problems. MINOS (Modular In-core Nonlinear Optimization System) may be used for linear programming, quadratic programming, and more general objective functions and constraints, and for finding a feasible point for a set of linear or nonlinear equalities and inequalities. MINOS was first developed by Bruce Murtagh and Michael Saunders, mostly at the Systems Optimization Laboratory in the Department of Operations Research at Stanford University. In 1985, Saunders was awarded the inaugural Orchard-Hays prize by the Mathematical Programming Society (now the Mathematical Optimization Society) for his work on MINOS. Despite being one of the first general-purpose constrained optimization solvers to emerge, the package remains heavily used. MINOS is supported in the AIMMS, AMPL, APMonitor, GAMS, and TOMLAB modeling systems. In addition, it remains one of the top-used solvers on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality. Its objective function is a real-valued affine (linear) function defined on this polyhedron. A linear programming algorithm finds a point in the polytope where this function has the smallest (or largest) value if such a point exists. Linear programs are problems that can be expressed in canonical form as : \begin & \t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Algebraic Equation
In electrical engineering, a differential-algebraic system of equations (DAEs) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. In mathematics these are examples of ``differential algebraic varieties'' and correspond to ideals in differential polynomial rings (see the article on differential algebra for the algebraic setup. We can write these differential equations for a dependent vector of variables ''x'' in one independent variable ''t'', as ::F(\dot x(t),\, x(t),\,t)=0 When considering these symbols as functions of a real variable (as is the case in applications in electrical engineering or control theory) we look at x: ,bto\R^n as a vector of dependent variables x(t)=(x_1(t),\dots,x_n(t)) and the system has as many equations, which we consider as functions F=(F_1,\dots,F_n):\R^\to\R^n. They are distinct from ordinary differential equation (ODE) in that a DAE is not completely solvable for the der ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Programming
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems. If some decision variables are not discrete, the problem is known as a mixed-integer programming problem. Canonical and standard form for ILPs In integer linear programming, the ''canonical form'' is distinct from the ''standard form''. An integer linear program in canonical form is expressed thus (note that it is the \mathbf vector which is to be decided): : \begin & \text && \mathbf^\mathrm \mathbf\\ & \text && A \mathbf \le \mathbf, \\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
