This constrained optimization problem is solved by using the Sequential Least-Squares Quadratic Programming (SLSQP), where a nonlinear constrained optimization is replaced by a standard quadratic program
with a quadratic approximation of the Lagrange function and linear approximation of the constraints .
Solving a linear program is much easier and faster than solving a quadratic program
The previous optimization problem is a convex quadratic program
which can be solved by using the well-known Lagrange multiplier method.
The maxcut problem can be formulated as the integer quadratic program
Therefore, the problem can be formulated as an integer quadratic program in n [multiplied by] m assignment variables.
However, minimizing the average weighted completion time forces quadratic terms and leads to the following integer quadratic program (IQP):
Recently, a new but important linear conic tool called completely positive programming (CPP) has been used to study the nonconvex quadratic program with linear and binary constraints.
Burer, "On the copositive representation of binary and continuous nonconvex quadratic programs," Mathematical Programming, vol.
The optimal solution of NLS can be gotten by solving quadratic program
and its dual problem.
The profits of the supplier, the local distributor (LD), and the external distributor (ED) can be formulated as three quadratic programs
that maximize the profits of three agents.
A parallel solver for large quadratic programs
in training support vector machines, Parallel Computing29(4): 535-551.
These functions allow FabRunner to cast solutions of control problems as either quadratic programs
or non-linear programs, depending on the problem requirements.