Sequential quadratic programming

<p>Sequential quadratic programming (SQP) is an <a href="/facts/Iterative_method/uKMAJhEh">iterative method</a> for <a href="/facts/Nonlinear_programming/cSXGuX2m">constrained nonlinear optimization</a>, also known as Lagrange-Newton method. SQP methods are used on <a href="/facts/Mathematics/pxTouaz4">mathematical</a> problems for which the <a href="/facts/Objective_function/xv5ozuhl">objective function</a> and the constraints are twice <a href="/facts/Continuously_differentiable/jQqTgLk1">continuously differentiable</a>, but not necessarily convex.
</p><p>SQP methods solve a sequence of optimization subproblems, each of which optimizes a quadratic model of the objective subject to a linearization of the constraints. If the problem is unconstrained, then the method reduces to <a href="/facts/Newton%2527s_method/VlRhI2FL">Newton's method</a> for finding a point where the gradient of the objective vanishes.  If the problem has only equality constraints, then the method is equivalent to applying <a href="/facts/Newton%2527s_method/VlRhI2FL">Newton's method</a> to the first-order optimality conditions, or <a href="/facts/Karush%25E2%2580%2593Kuhn%25E2%2580%2593Tucker_conditions/ly7g2zST">Karush–Kuhn–Tucker conditions</a>, of the problem.
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Sequential quadratic programming open-in-new

Sequential quadratic programming