| ## Standard Forms and Geometry Up | Next ### Linear Programs A linear program (or LP, for short) is an optimization problem in the standard form introduced here: where the objective function , and the constraint functions , , are all affine. Since affine functions are linear plus constant, and constant terms in the objective do not matter, we can always assume that is actually linear. Examples: An LP in two variables. A drug production problem. ### Quadratic programs A quadratic program (or QP, for short) is an optimization problem in the standard form above, where: the constraint functions , , are all affine, as in LP; the objective function is quadratic convex, that is, its values can be expressed as for some vector and ( is symmetric, and all of its eigenvalues is non-negative). ### Geometry Each constraint in an LP is a single affine inequality in the decision vector . Hence, each constraint says that the decision vector should lie in a half-space. Taken together, the constraints require that should like in the intersection of those half-spaces, that is, a polyhedron. The geometry of LP is to minimize a linear function over a polyhedron. The geometry of QP is to minimize a convex (bowl-shaped) quadratic function over a polyhedron. Examples: A quadratic program in two variables.