| # LP and QP in conic form The LP can always be represented in the conic form for appropriate matrix and vector . To prove this, we introduce three new sets of non-negative variables: , which represents the constraints, and , which contain the positive and negative parts of vector . We have , with and . The constraint then reads . Let us define the new variable / The relationship between can then be expressed as , with The objective of the original problem can be written as , with Putting this together, we express the original LP as claimed