Linear programming and Quadratic programming

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Difference between Linear programming and Quadratic programming

Linear programming vs. Quadratic 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. Quadratic programming (QP) is the process of solving a special type of mathematical optimization problem—specifically, a (linearly constrained) quadratic optimization problem, that is, the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables.

AIMMS

is a prescriptive analytics software company with offices in the Netherlands, United States, China and Singapore.

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Algebraic modeling language

Algebraic modeling languages (AML) are high-level computer programming languages for describing and solving high complexity problems for large scale mathematical computation (i.e. large scale optimization type problems).

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AMPL

A Mathematical Programming Language (AMPL) is an algebraic modeling language to describe and solve high-complexity problems for large-scale mathematical computing (i.e., large-scale optimization and scheduling-type problems).

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APMonitor

Advanced process monitor (APMonitor), is a modeling language for differential algebraic (DAE) equations.

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Convex optimization

Convex optimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.

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CPLEX

IBM ILOG CPLEX Optimization Studio (often informally referred to simply as CPLEX) is an optimization software package.

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Duality (optimization)

In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem.

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Ellipsoid method

In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions.

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FICO Xpress

The FICO Xpress Optimizer is a commercial optimization solver for linear programming (LP), mixed integer linear programming (MILP), convex quadratic programming (QP), convex quadratically constrained quadratic programming (QCQP), second-order cone programming (SOCP) and their mixed integer counterparts.

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General Algebraic Modeling System

The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical optimization.

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Gurobi

The Gurobi Optimizer is a commercial optimization solver for linear programming (LP), quadratic programming (QP), quadratically constrained programming (QCP), mixed integer linear programming (MILP), mixed-integer quadratic programming (MIQP), and mixed-integer quadratically constrained programming (MIQCP).

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IMSL Numerical Libraries

IMSL (International Mathematics and Statistics Library) is a commercial collection of software libraries of numerical analysis functionality that are implemented in the computer programming languages C, Java, C#.NET, and Fortran.

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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.

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Interior-point method

Interior-point methods (also referred to as barrier methods) are a certain class of algorithms that solve linear and nonlinear convex optimization problems.

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Leonid Khachiyan

Leonid Genrikhovich Khachiyan (Լեոնիդ Գենրիխովիչ Խաչիյան; Леонид Генрихович Хачиян; May 3, 1952 – April 29, 2005) was a Soviet mathematician of Armenian descent who taught Computer Science at Rutgers University.

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Maple (software)

Maple is a symbolic and numeric computing environment, and is also a multi-paradigm programming language.

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Mathematical optimization

In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.

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MATLAB

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks.

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Microsoft Excel

Microsoft Excel is a spreadsheet developed by Microsoft for Windows, macOS, Android and iOS.

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MOSEK

MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constraint, conic and convex nonlinear mathematical optimization problems.

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NAG Numerical Library

The NAG Numerical Library is a software product developed and sold by The Numerical Algorithms Group.

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Nonlinear programming

In mathematics, nonlinear programming is the process of solving an optimization problem defined by a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear.

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NP-hardness

NP-hardness (''n''on-deterministic ''p''olynomial-time hardness), in computational complexity theory, is the defining property of a class of problems that are, informally, "at least as hard as the hardest problems in NP".

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Numerical Algorithms Group

The Numerical Algorithms Group (NAG) is a software company which provides methods for the solution of mathematical and statistical problems, and offers services to users of High performance computing (HPC) systems.

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Proceedings of the USSR Academy of Sciences

The Proceedings of the USSR Academy of Sciences (Доклады Академии Наук СССР, Doklady Akademii Nauk SSSR (DAN SSSR), Comptes Rendus de l'Académie des Sciences de l'URSS) was a Soviet journal that was dedicated to publishing original, academic research papers in physics, mathematics, chemistry, geology, and biology.

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R (programming language)

R is a programming language and free software environment for statistical computing and graphics that is supported by the R Foundation for Statistical Computing.

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SAS (software)

SAS (previously "Statistical Analysis System") is a software suite developed by SAS Institute for advanced analytics, multivariate analyses, business intelligence, data management, and predictive analytics.

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Simplex algorithm

In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

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TOMLAB

The TOMLAB Optimization Environment is a modeling platform for solving applied optimization problems in MATLAB.

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Transpose

In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal, that is it switches the row and column indices of the matrix by producing another matrix denoted as AT (also written A′, Atr, tA or At).

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Wolfram Mathematica

Wolfram Mathematica (usually termed Mathematica) is a modern technical computing system spanning most areas of technical computing — including neural networks, machine learning, image processing, geometry, data science, visualizations, and others.

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