function [errmsg,Z,X,t,c,fail] = BNB18(fun,x0,xstat,xl,xu,A,B,Aeq,Beq,nonlcon,tts,options1,options2,maxSQPit,varargin);
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% Minimize F(x)
%subject to: xlb <= x <=xub
lookinto% A*x <= B
% Aeq*x=Beq
% C(x)<=0
% Ceq(x)=0
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%[errmsg,Z,X]=BNB18('fun',x0,xstat,xl,xu,A,B,Aeq,Beq,'nonlcon',tts)
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% max x1*x2*x3
% -x1+2*x2+2*x3>=0
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% x1+2*x2+2*x3<=72
% 10<=x2<=20
% x1-x2=10
% ÏÈд Mº¯Êýdiscfun.m
% function f=discfun(x)
chen guangcheng% f=-x(1)*x(2)*x(3);
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% clear;x0=[25,15,10]';xstat=[1 1 1]';
% xl=[20 10 -10]';xu=[30 20 20]';
% A=[1 -2 -2;1 2 2];B=[0 72]';Aeq=[1 -1 0];Beq=10;
% [err,Z,X]=BNB18('discfun',x0,xstat,xl,xu,A,B,Aeq,Beq);
mouevent% XMAX=X',ZMAX=-Z
%
% BNB18 Finds the constrained minimum of a function of veral possibly integer variables.
% Usage: [errmsg,Z,X,t,c,fail] =
% BNB18(fun,x0,xstatus,xlb,xub,A,B,Aeq,Beq,nonlcon,ttings,options1,options2,maxSQPiter,P1,P2,...)
%
% BNB solves problems of the form:
% Minimize F(x) subject to: xlb <= x0 <=xub
% A*x <= B Aeq*x=Beq
% C(x)<=0 Ceq(x)=0
% x(i) is continuous for xstatus(i)=0
% x(i) integer for xstatus(i)= 1
% x(i) fixed for xstatus(i)=2
%
% BNB us:
% Optimization Toolbox Version 2.0 (R11) 09-Oct-1998
% From this toolbox fmincon.m is called. For more info type help fmincon.
%
% fun is the function to be minimized and should return a scalar. F(x)=feval(fun,x).
% x0 is the starting point for x. x0 should be a column vector.
% xstatus is a column vector describing the status of every variable x(i).
% xlb and xub are column vectors with lower and upper bounds for x.
% A and Aeq are matrices for the linear constrains.
% B and Beq are column vectors for the linear constrains.
% nonlcon is the function for the nonlinear constrains.
% [C(x);Ceq(x)]=feval(nonlcon,x). Both C(x) and Ceq(x) should be column vectors.
%
% errmsg is a string containing an error message if BNB found an error in the input.
% Z is the scalar result of the minimization, X the values of the accompanying variables.
% t is the time elapd while the algorithm BNB has run, c is the number of BNB cycles and
制版费英文% fail is the number of unsolved leaf sub-problems.
%
% ttings is a row vector with ttings for BNB:
% ttings(1) (standard 0) if 1: u pha 1 by relaxation. This sometimes makes the algorithm
% faster, becau pha 1 means the algorithm first checks if there is a feasible solution
% for a sub-problem before trying to find a best solution. If there is no feasible solution BNB
% will not try to find a best solution.
% ttings(2) (standard 0) if 1: if the sub-problem did not converge do not branch. If a sub-
% problem did not converge this means BNB did not find a solution for it. Normally BNB will
% branch the problem so it can try again to find a solution.
% A sub-problem that is a leaf of the branch-and-bound-three can not be branched. If such
% a problem does not converge it will be considered unfeasible and the parameter fail will be
% raid by one.
% ttings(3) (standard 0) if 1: if 1 a sub-problem that did not converge but did return a feasible
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% point will be considered convergent. This might be uful if fmincon is having a hard time with
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% a certain problem but you do want some results.
% options1 and options2 are options structures for pha 1 and pha 2.
% For details about the options structure type help optimt.
