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.
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.
Linear programming relaxationIn mathematics, the relaxation of a (mixed) integer linear program is the problem that arises by removing the integrality constraint of each variable. For example, in a 0–1 integer program, all constraints are of the form The relaxation of the original integer program instead uses a collection of linear constraints The resulting relaxation is a linear program, hence the name.
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.
Team sportA team sport includes any sport where individuals are organized into opposing teams which compete to win or cooperate to entertain their audience. Team members act together towards a shared objective. This can be done in a number of ways such as outscoring the opposing team. Team members set goals, make decisions, communicate, manage conflict, and solve problems in a supportive, trusting atmosphere in order to accomplish their objectives.
Environmental artEnvironmental art is a range of artistic practices encompassing both historical approaches to nature in art and more recent ecological and politically motivated types of works. Environmental art has evolved away from formal concerns, for example monumental earthworks using earth as a sculptural material, towards a deeper relationship to systems, processes and phenomena in relationship to social concerns. Integrated social and ecological approaches developed as an ethical, restorative stance emerged in the 1990s.
Public artPublic art is art in any media whose form, function and meaning are created for the general public through a public process. It is a specific art genre with its own professional and critical discourse. Public art is visually and physically accessible to the public; it is installed in public space in both outdoor and indoor settings. Public art seeks to embody public or universal concepts rather than commercial, partisan, or personal concepts or interests.
ArtArt is a diverse range of human activity, and resulting product, that involves creative or imaginative talent expressive of technical proficiency, beauty, emotional power, or conceptual ideas. There is no generally agreed definition of what constitutes art, and its interpretation has varied greatly throughout history and across cultures. In the Western tradition, the three classical branches of visual art are painting, sculpture, and architecture.
Professional sportsIn professional sports, as opposed to amateur sports, participants receive payment for their performance. Professionalism in sport has come to the fore through a combination of developments. Mass media and increased leisure have brought larger audiences, so that sports organizations or teams can command large incomes. As a result, more sportspeople can afford to make sport their primary career, devoting the training time necessary to increase skills, physical condition, and experience to modern levels of achievement.
