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Bilinear Program
In mathematics, a bilinear program is a nonlinear optimization In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or st ... problem whose objective or constraint functions are bilinear. An example is the pooling problem. References Bilinear programat the Mathematical Programming Glossary. Mathematical optimization {{mathapplied-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear Optimization
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear. Applicability A typical non-convex problem is that of optimizing transportation costs by selection from a set of transportation methods, one or more of which exhibit economies of scale, with various connectivities and capacity constraints. An example would be petroleum product transport given a selection or combination of pipeline, rail tanker, road tanker, river barge, or coastal tankship. Owing to economic batch size the cost functions may have disconti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bilinear Form
In mathematics, a bilinear form is a bilinear map on a vector space (the elements of which are called '' vectors'') over a field ''K'' (the elements of which are called '' scalars''). In other words, a bilinear form is a function that is linear in each argument separately: * and * and The dot product on \R^n is an example of a bilinear form. The definition of a bilinear form can be extended to include modules over a ring, with linear maps replaced by module homomorphisms. When is the field of complex numbers , one is often more interested in sesquilinear forms, which are similar to bilinear forms but are conjugate linear in one argument. Coordinate representation Let be an - dimensional vector space with basis . The matrix ''A'', defined by is called the ''matrix of the bilinear form'' on the basis . If the matrix represents a vector with respect to this basis, and analogously, represents another vector , then: B(\mathbf, \mathbf) = \mathbf^\texts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pooling Problem
Pool may refer to: Water pool * Swimming pool, usually an artificial structure containing a large body of water intended for swimming * Reflecting pool, a shallow pool designed to reflect a structure and its surroundings * Tide pool, a rocky pool on an ocean shore that remains filled with seawater when the tide goes out * Salt pannes and pools, a water-retaining depression located within salt and brackish marshes * Plunge pool, a small, deep body of water * Stream pool, a quiet slow-moving portion of a stream * Spent fuel pool, a storage facility for used fuel rods from a nuclear reactor Sports and gambling * Pool (cards), the common pot for stakes or the stakes themselves in card games * Pool (dominoes), the stock or boneyard in dominoes * Pool (cue sports), a group of games played on a pool table * Pool (poker) or pot (poker), money wagered during a single hand of poker * Pool betting or parimutuel betting, a betting system in which all bets of a particular type are placed toge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |