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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.
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.
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.
In mathematical optimization theory, the linear complementarity problem (LCP) arises frequently in computational mechanics and encompasses the well-known quadratic programming as a special case. It was proposed by Cottle and Dantzig in 1968.
IMSL Numerical Libraries – linear, quadratic, nonlinear, and sparse QP and LP optimization algorithms implemented in standard programming languages C, Java, C# .NET, Fortran, and Python. IOSO – (Indirect optimization on the basis of Self-Organization) a multi-objective, multidimensional nonlinear optimization technology.
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.
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 ...
Solver with an API for large scale optimization of linear, integer, quadratic, conic and general nonlinear programs with stochastic programming extensions. It offers a global optimization procedure for finding guaranteed globally optimal solution to general nonlinear programs with continuous and discrete variables.