Linear programmingLinear 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.
Windows VistaWindows Vista is a major release of the Windows NT operating system developed by Microsoft as the direct successor to Windows XP, which was released in 2001. At the time, this 5-year gap was the longest time span between successive releases of Microsoft's Windows desktop operating systems. Development was finished on November 8, 2006, and over the following three months, it was released in stages to computer hardware and software manufacturers, business customers, and retail channels.
Windows MobileWindows Mobile was a family of mobile operating systems developed by Microsoft for smartphones and personal digital assistants. Its origin dated back to Windows CE in 1996, though Windows Mobile itself first appeared in 2000 as Pocket PC 2000 which ran on Pocket PC PDAs. It was renamed "Windows Mobile" in 2003, at which point it came in several versions (similar to the desktop versions of Windows) and was aimed at business and enterprise consumers.
Travelling salesman problemThe travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP.
Vehicle routing problemThe vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers?" It generalises the travelling salesman problem (TSP). It first appeared in a paper by George Dantzig and John Ramser in 1959, in which the first algorithmic approach was written and was applied to petrol deliveries. Often, the context is that of delivering goods located at a central depot to customers who have placed orders for such goods.
Integer programmingAn 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.
Cutting-plane methodIn 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.
Windows MeWindows Millennium Edition, or Windows Me (marketed with the pronunciation of the pronoun "me"), often capitalized as Windows ME, is an operating system developed by Microsoft as part of its Windows 9x family of Microsoft Windows operating systems. It is the successor to Windows 98, and was released to manufacturing on June 19, 2000, and then to retail on September 14, 2000. It was Microsoft's main operating system for home users until the introduction of its successor Windows XP in October 2001.
Microsoft WindowsMicrosoft Windows is a group of several proprietary graphical operating system families developed and marketed by Microsoft. Each family caters to a certain sector of the computing industry. For example, Windows NT for consumers, Windows Server for servers, and Windows IoT for embedded systems. Defunct Windows families include Windows 9x, Windows Mobile, and Windows Phone. The first version of Windows was released on November 20, 1985, as a graphical operating system shell for MS-DOS in response to the growing interest in graphical user interfaces (GUIs).
Windows RuntimeWindows Runtime (WinRT) is a platform-agnostic component and application architecture first introduced in Windows 8 and Windows Server 2012 in 2012. It is implemented in C++ and officially supports development in C++ (via C++/WinRT, C++/CX or WRL), Rust/WinRT, Python/WinRT, JavaScript-TypeScript, and the managed code languages C# and Visual Basic .NET (VB.NET). WinRT is not a runtime in a traditional sense but rather a language-independent application binary interface based on COM to allow APIs to be consumed from multiple languages, with services usually provided by a full-blown runtime, such as type activation.
