Standard Forms and GeometryLinear ProgramsA linear program (or LP, for short) is an optimization problem in the standard form introduced here:
Since affine functions are linear plus constant, and constant terms in the objective do not matter, we can always assume that Examples: Quadratic programsA quadratic program (or QP, for short) is an optimization problem in the standard form above, where:
GeometryEach constraint in an LP is a single affine inequality in the decision vector 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: |