A New Spatial Branch and Bound Algorithm for Quadratic Program with One Quadratic Constraint and Linear Constraints

Algorithm 1

A spatial branch-and-bound algorithm (SOCP_BB) for solving (1).

	Require: An instance of (1) and a given error tolerance . Set iteration step , the upper bound and .
(1)	Solve (11) for and .
(2)	If (11) is infeasible, then
(3)	(1) is infeasible and terminate.
(4)	end if
(5)	Solve (10) over for its optimal objective function value and optimal solution . Let and .
(6)	Construct a set and insert into it.
(7)	loop
(8)	if then
(9)	return and terminate.
(10)	end if
(11)	Choose a node from , denoted as such that and remove it from .
(12)	if , then
(13)	return and terminate.
(14)	end if
(15)	Set .
(16)	Choose .
(17)	Construct the box by setting , , and construct the box by setting , , .
(18)	if (10) over is feasible, then
(19)	Solve (10) over for its optimal objective function value and optimal solution . Denote .
(20)	if , then
(21)	and .
(22)	end if
(23)	if , then
(24)	insert into .
(25)	end if
(26)	end if
(27)	if (10) over is feasible, then
(28)	Solve (10) over for its optimal objective function value and optimal solution . Denote .
(29)	if , then
(30)	and .
(31)	end if
(32)	if , then
(33)	insert into .
(34)	end if
(35)	end if
(36)	end loop