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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.
Sequential minimal optimization (SMO) is an algorithm for solving the quadratic programming (QP) problem that arises during the training of support-vector machines (SVM). It was invented by John Platt in 1998 at Microsoft Research. [1] SMO is widely used for training support vector machines and is implemented by the popular LIBSVM tool.
However, even for a nonconvex QCQP problem a local solution can generally be found with a nonconvex variant of the interior point method. In some cases (such as when solving nonlinear programming problems with a sequential QCQP approach) these local solutions are sufficiently good to be accepted.
This is not convex, and in general much more difficult than regular linear programming. Quadratic programming allows the objective function to have quadratic terms, while the feasible set must be specified with linear equalities and inequalities. For specific forms of the quadratic term, this is a type of convex programming.
For example, in solving the linear programming problem, the active set gives the hyperplanes that intersect at the solution point. In quadratic programming , as the solution is not necessarily on one of the edges of the bounding polygon, an estimation of the active set gives us a subset of inequalities to watch while searching the solution ...
Coffee beans are hitting record high prices not seen in nearly 50 years after difficult growing seasons among some of the world's top producing regions. Earlier this week, the Wall Street Journal ...
The Fortran subroutine NLPQLP, a newer [when?] version of NLPQL, solves smooth nonlinear programming problems by a sequential quadratic programming (SQP) algorithm. The new version is specifically tuned to run under distributed systems.