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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. Its feasible region is a convex polytope, which is a set defined as the ...
Multi-objective linear programming is a subarea of mathematical optimization. A multiple objective linear program (MOLP) is a linear program with more than one objective function. An MOLP is a special case of a vector linear program. Multi-objective linear programming is also a subarea of Multi-objective optimization .
In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions. For a polyhedron and a vector , is a basic solution if: All the equality constraints defining. P {\displaystyle P} are active at.
The dual of a given linear program (LP) is another LP that is derived from the original (the primal) LP in the following schematic way: The objective direction is inversed – maximum in the primal becomes minimum in the dual and vice versa. The weak duality theorem states that the objective value of the dual LP at any feasible solution is ...
GLIM (software) GLIM (an acronym for Generalized Linear Interactive Modelling) is a statistical software program for fitting generalized linear models (GLMs). It was developed by the Royal Statistical Society's Working Party on Statistical Computing (later renamed the GLIM Working Party), [1] chaired initially by John Nelder. [2]
Nonlinear programming. In mathematics, nonlinear programming ( NLP) is the process of solving an optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective ...
Linear programming relaxation. In 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 ...
Successive linear programming. Successive Linear Programming ( SLP ), also known as Sequential Linear Programming, is an optimization technique for approximately solving nonlinear optimization problems. [1] It is related to, but distinct from, quasi-Newton methods . Starting at some estimate of the optimal solution, the method is based on ...