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 .
To enable fast and efficient computation, we formulate the optimization problem as a quadratic program
. We also examine how the inclusion of cash management bills would affect costs, using a heuristic approach based on shadow prices derived from the quadratic programming solution.
(12) Solve the quadratic program
(linear program with quadratic objective function).
Huang, "A new class of interval projection neural networks for solving interval quadratic program
," Chaos, Solitons and Fractals, vol.
After the transformation, the original problem was transformed into an equivalent convex quadratic program
Recently, many modern heuristics stochastic search algorithms such as genetic algorithm (GA) , evolutionary programming (EP) , tabu search (TS) , particle swam optimization (PSO) [9, 10], differential evolution algorithm (DE) [11-21], biogeography-based optimization (BBO) , chaotic self-adaptive differential harmony search algorithm (CSADHS) , quadratically constrained quadratic program
method (QCQP) , Krill herd algorithm (KHA) , and harmony search with new pitch (NPAHS)  have shown great potentials in solving the nonlinear ELD or DED problems.
Solving a linear program is much easier and faster than solving a quadratic program
. The optimal portfolio consists of at most 2T + 2 assets regardless of the size, n while Markowitz model may consist of n assets.
The previous optimization problem is a convex quadratic program
which can be solved by using the well-known Lagrange multiplier method.
Therefore, the problem can be formulated as an integer quadratic program
in n [multiplied by] m assignment variables.
For an iterative point [x.sup.k], a new quadratic program
(QP) subproblem is given by
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.
 formulated the GAP as a mixed binary quadratic program
with minimizing the slack time overall variance as the objective function; an assumption has been stated such that the flights are sequenced with the smallest arrival time.