| ## Other Standard Forms Up | Back ### Inequality form As seen here, a function is affine if and only if it can be expressed via the scalar product, as for some appropriate vector and scalar . Hence, a linear program can be expressed as for some appropriate vectors and scalars . We can use the component-wise inequality convention and put the above problem into the inequality standard form: where Similarly, for QP a standard form is ### QPs with equality constraints In LP or QP models, we can have equality constraints as well. For example, the LP where , define the equality constraints, can be put in standard inequality form, as ### Conic form A problem of the form is an LP. Conversely, any LP can be put in the above form (Proof). A similar result holds for QP. (The reason of the term ‘‘conic’’ comes from the fact that the above problem is part of a more general class known as conic problems, in which the sign constraints on the variables are replaced with , where is a cone.) The above form is useful to develop theory and algorithms for LP, as it puts all the ‘‘data’’ of the problem into the linear objective and the linear equality constraints, while the inequalities have a very simple, data-independent structure.