Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions. Specifically,one seeks to optimize a multivariate quadratic function subject to linear constraints on the variables. Quadratic programming is a type of nonlinear programming.
Linear programming (LP),also called linear optimization,is a method to achieve the best outcome in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming.
Mathematical optimization or mathematical programming is the selection of a best element,with regard to some criteria,from some set of available alternatives. It is generally divided into two subfields:discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics,and the development of solution methods has been of interest in mathematics for centuries.
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 are linear.
In mathematical optimization,the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities,termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems,as well as to solve general,not necessarily differentiable convex optimization problems. The use of cutting planes to solve MILP was introduced by Ralph E. Gomory.
Computational Infrastructure for Operations Research (COIN-OR),is a project that aims to "create for mathematical software what the open literature is for mathematical theory." The open literature provides the operations research (OR) community with a peer-review process and an archive. Papers in operations research journals on mathematical theory often contain supporting numerical results from computational studies. The software implementations,models,and data used to produce the numerical results are typically not published. The status quo impeded researchers needing to reproduce computational results,make fair comparisons,and extend the state of the art.
The TOMLAB Optimization Environment is a modeling platform for solving applied optimization problems in MATLAB.
Algebraic modeling languages (AML) are high-level computer programming languages for describing and solving high complexity problems for large scale mathematical computation. One particular advantage of some algebraic modeling languages like AIMMS,AMPL,GAMS,Gekko,MathProg,Mosel,and OPL is the similarity of their syntax to the mathematical notation of optimization problems. This allows for a very concise and readable definition of problems in the domain of optimization,which is supported by certain language elements like sets,indices,algebraic expressions,powerful sparse index and data handling variables,constraints with arbitrary names. The algebraic formulation of a model does not contain any hints how to process it.
The Zuse Institute Berlin is a research institute for applied mathematics and computer science on the campus of Freie Universität Berlin in Dahlem,Berlin,Germany.
AIMMS is a prescriptive analytics software company with offices in the Netherlands,United States and Singapore.
George Lann Nemhauser is an American operations researcher,the A. Russell Chandler III Chair and Institute Professor of Industrial and Systems Engineering at the Georgia Institute of Technology and the former president of the Operations Research Society of America.
Egon Balas was an applied mathematician and a professor of industrial administration and applied mathematics at Carnegie Mellon University. He was the Thomas Lord Professor of Operations Research at Carnegie Mellon's Tepper School of Business and did fundamental work in developing integer and disjunctive programming.
Laurence Alexander Wolsey is a Belgian-English mathematician working in the field of integer programming. His mother Anna Wolsey-Mautner was the daughter of the Viennese Industrialist Konrad David Mautner. He is a former president and research director of the Center for Operations Research and Econometrics (CORE) at Universitécatholique de Louvain in Belgium. He is professor emeritus of applied mathematics at the engineering school of the same university.
Michel Louis Balinski was an American and French applied mathematician,economist,operations research analyst and political scientist. Educated in the United States,from 1980 he lived and worked in France. He was known for his work in optimisation,convex polyhedra,stable matching,and the theory and practice of electoral systems,jury decision,and social choice. He was Directeur de Recherche de classe exceptionnelle (emeritus) of the C.N.R.S. at the École Polytechnique (Paris). He was awarded the John von Neumann Theory Prize by INFORMS in 2013.
Convex Over and Under ENvelopes for Nonlinear Estimation (Couenne) is an open-source library for solving global optimization problems,also termed mixed integer nonlinear optimization problems. A global optimization problem requires to minimize a function,called objective function,subject to a set of constraints. Both the objective function and the constraints might be nonlinear and nonconvex. For solving these problems,Couenne uses a reformulation procedure and provides a linear programming approximation of any nonconvex optimization problem.
JuMP is an algebraic modeling language and a collection of supporting packages for mathematical optimization embedded in the Julia programming language. JuMP is used by companies,government agencies,academic institutions,software projects,and individuals to formulate and submit optimization problems to third‑party solvers. JuMP has been specifically applied to problems in the field of operations research.
Gérard Pierre Cornuéjols is the IBM University Professor of Operations Research in the Carnegie Mellon University Tepper School of Business and professor at Aix-Marseille University. His research interests include facility location,integer programming,balanced matrices,and perfect graphs.
Maria Grazia Speranza is an Italian applied mathematician and operations researcher. Her research involves the application of mathematical optimization to problems including portfolio optimization and the combination of inventory management with vehicle routing.
The EURO Advanced Tutorials in Operational Research are a series of short books devoted to advanced topics in Operational Research that are not available in textbooks. The scope of a Tutorial is to provide more detail about advanced topics in a relevant field to researchers and practitioners. The Book Series was established in 2014 and is published by Springer Science+Business Media. It is an official publication of the Association of European Operational Research Societies.
Shmuel Onn is a mathematician,Professor of Operations Research and Dresner Chair at the Technion - Israel Institute of Technology. He is known for his contributions to integer programming and nonlinear combinatorial optimization.
