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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.
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.
A hierarchy of convex optimization problems. (LP: linear programming, QP: quadratic programming, SOCP second-order cone program, SDP: semidefinite programming, CP: conic optimization.) Linear programming problems are the simplest convex programs. In LP, the objective and constraint functions are all linear. Quadratic programming are the next ...
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.
Popular solver with an API for several programming languages. Free for academics. MOSEK: A solver for large scale optimization with API for several languages (C++, java, .net, Matlab and python) TOMLAB: Supports global optimization, integer programming, all types of least squares, linear, quadratic and unconstrained programming for MATLAB.
Quasi-Newton methods, on the other hand, can be used when the Jacobian matrices or Hessian matrices are unavailable or are impractical to compute at every iteration. Some iterative methods that reduce to Newton's method, such as sequential quadratic programming, may also be considered quasi-Newton methods.
It was the first quasi-Newton method to generalize the secant method to a multidimensional problem. This update maintains the symmetry and positive definiteness of the Hessian matrix . Given a function f ( x ) {\displaystyle f(x)} , its gradient ( ∇ f {\displaystyle \nabla f} ), and positive-definite Hessian matrix B {\displaystyle B} , the ...