Simplex algorithmIn mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming. The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. Simplices are not actually used in the method, but one interpretation of it is that it operates on simplicial cones, and these become proper simplices with an additional constraint. The simplicial cones in question are the corners (i.e., the neighborhoods of the vertices) of a geometric object called a polytope.
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.
Feasible regionIn mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.
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.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, 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.
SimplexIn geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, a 0-dimensional simplex is a point, a 1-dimensional simplex is a line segment, a 2-dimensional simplex is a triangle, a 3-dimensional simplex is a tetrahedron, and a 4-dimensional simplex is a 5-cell. Specifically, a k-simplex is a k-dimensional polytope which is the convex hull of its k + 1 vertices.
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.
VideoVideo is an electronic medium for the recording, copying, playback, broadcasting, and display of moving media. Video was first developed for mechanical television systems, which were quickly replaced by cathode-ray tube (CRT) systems which, in turn, were replaced by flat panel displays of several types. Video systems vary in display resolution, aspect ratio, refresh rate, color capabilities and other qualities. Analog and digital variants exist and can be carried on a variety of media, including radio broadcasts, magnetic tape, optical discs, , and network streaming.
Video gameA video game or computer game is an electronic game that involves interaction with a user interface or input device (such as a joystick, controller, keyboard, or motion sensing device) to generate visual feedback from a display device, most commonly shown in a video format on a television set, computer monitor, flat-panel display or touchscreen on handheld devices, or a virtual reality headset. Most modern video games are audiovisual, with audio complement delivered through speakers or headphones, and sometimes also with other types of sensory feedback (e.
High-definition videoHigh-definition video (HD video) is video of higher resolution and quality than standard-definition. While there is no standardized meaning for high-definition, generally any video image with considerably more than 480 vertical scan lines (North America) or 576 vertical lines (Europe) is considered high-definition. 480 scan lines is generally the minimum even though the majority of systems greatly exceed that. Images of standard resolution captured at rates faster than normal (60 frames/second North America, 50 fps Europe), by a high-speed camera may be considered high-definition in some contexts.
Music videoA music video, sometimes abbreviated to MV or M/V, is a video that integrates a song or an album with imagery that is produced for promotional or musical artistic purposes. Modern music videos are primarily made and used as a music marketing device intended to promote the sale of music recordings. These videos are typically shown on music television and on streaming video sites like YouTube, or more rarely shown theatrically. They can be commercially issued on home video, either as video albums or video singles.
MP3MP3 (formally MPEG-1 Audio Layer III or MPEG-2 Audio Layer III) is a coding format for digital audio developed largely by the Fraunhofer Society in Germany under the lead of Karlheinz Brandenburg, with support from other digital scientists in the United States and elsewhere. Originally defined as the third audio format of the MPEG-1 standard, it was retained and further extended — defining additional bit-rates and support for more audio channels — as the third audio format of the subsequent MPEG-2 standard.
Digital audioDigital audio is a representation of sound recorded in, or converted into, digital form. In digital audio, the sound wave of the audio signal is typically encoded as numerical samples in a continuous sequence. For example, in CD audio, samples are taken 44,100 times per second, each with 16-bit sample depth. Digital audio is also the name for the entire technology of sound recording and reproduction using audio signals that have been encoded in digital form.
