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Sequential linear-quadratic programming (SLQP) is an iterative method for nonlinear optimization problems where objective function and constraints are twice continuously differentiable. Similarly to sequential quadratic programming (SQP), SLQP proceeds by solving a sequence of optimization subproblems.
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.
Successive Linear Programming (SLP), also known as Sequential Linear Programming, is an optimization technique for approximately solving nonlinear optimization problems. [1] It is related to, but distinct from, quasi-Newton methods .
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. Quadratic programming is a type of nonlinear programming.
Since the 1970s, sequential quadratic programming (SQP) and interior point methods (IPM) have been given more attention, in part because they more easily use sparse matrix subroutines from numerical software libraries, and in part because IPMs possess proven complexity results via the theory of self-concordant functions.
There are two main relaxations of QCQP: using semidefinite programming (SDP), and using the reformulation-linearization technique (RLT). For some classes of QCQP problems (precisely, QCQPs with zero diagonal elements in the data matrices), second-order cone programming (SOCP) and linear programming (LP) relaxations providing the same objective value as the SDP relaxation are available.
Successive linear programming (SLP) — replace problem by a linear programming problem, solve that, and repeat; Sequential quadratic programming (SQP) — replace problem by a quadratic programming problem, solve that, and repeat; Newton's method in optimization. See also under Newton algorithm in the section Finding roots of nonlinear equations
An interior point method was discovered by Soviet mathematician I. I. Dikin in 1967. [1] The method was reinvented in the U.S. in the mid-1980s. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm, [2] which runs in provably polynomial time (() operations on L-bit numbers, where n is the number of variables and constants), and is also very ...