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Sequential linear-quadratic programming
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<p>Sequential linear-quadratic programming (SLQP) is an <a href="/facts/Iterative_method/uKMAJhEh">iterative method</a> for <a href="/facts/Nonlinear_programming/cSXGuX2m">nonlinear optimization problems</a> where <a href="/facts/Objective_function/xv5ozuhl">objective function</a> and constraints are twice <a href="/facts/Continuously_differentiable/jQqTgLk1">continuously differentiable</a>. Similarly to <a href="/facts/Sequential_quadratic_programming/3QUzYBps">sequential quadratic programming</a> (SQP), SLQP proceeds by solving a sequence of optimization subproblems. The difference between the two approaches is that: </p> <ul><li>in SQP, each subproblem is a <a href="/facts/Quadratic_program/ct4RIUgs">quadratic program</a>, with a quadratic model of the objective subject to a linearization of the constraints</li> <li>in SLQP, two subproblems are solved at each step: a <a href="/facts/Linear_program/GduXFQxT">linear program</a> (LP) used to determine an <a href="/facts/Active_set/WLtXKtq9">active set</a>, followed by an equality-constrained quadratic program (EQP) used to compute the total step</li></ul> <p>This decomposition makes SLQP suitable to large-scale optimization problems, for which efficient LP and EQP solvers are available, these problems being easier to scale than full-fledged quadratic programs. </p><p>It may be considered related to, but distinct from, <a href="/facts/Quasi-Newton_method/1YX1vMRa">quasi-Newton methods</a>. </p>