Quadratic programming (QP)

Quadratic programming (QP) is the problem of optimizing a quadratic objective function and is one of the simplests form of non-linear programming. The objective function can contain bilinear or up to second order polynomial terms, and the constraints are linear and can be both equalities and inequalities.

QP is widely used in image and signal processing, to optimize financial portfolios, to perform the least-squares method of regression, to control scheduling in chemical plants, and in sequential quadratic programming, a technique for solving more complex non-linear programming problems.

The problem was first explored in the early 1950s, most notably by Princeton University’s Wolfe and Frank, who developed its theoretical background, and by Markowitz, who applied it to portfolio optimization, a subfield of finance.

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