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Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization which may be considered a quasi-Newton method.SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable, but not necessarily convex.
Quadratic programming (QP) is the process of solving certain mathematical optimization problems involving quadratic functions.Specifically, one seeks to optimize (minimize or maximize) a multivariate quadratic function subject to linear constraints on the variables.
In the EQP phase of SLQP, the search direction of the step is obtained by solving the following equality-constrained quadratic program: + + (,,).. + = + =Note that the term () in the objective functions above may be left out for the minimization problems, since it is constant.
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For each natural number the corresponding convex relaxation is known as the th level or -th round of the SOS hierarchy. The 1 {\textstyle 1} st round, when d = 1 {\textstyle d=1} , corresponds to a basic semidefinite program , or to sum-of-squares optimization over polynomials of degree at most 2 {\displaystyle 2} .