Sequential Quadratic Programming (SQP) is an iterative method for solving nonlinear optimization problems. It is particularly effective for nonlinear programming problems that have constraints. The fundamental idea behind SQP is to approximate the original nonlinear optimization problem with a series of quadratic programming (QP) subproblems, which are easier to solve.
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Sequential quadratic programming computes steps from a quadratic model of the optimization Lagrangian with linearized constraints. Its constrained Newton system couples a primal step and multiplier estimates. A line search or trust region then controls the use of that local model.