计算机问题求解一论题3-15 线性规划 2017年2月20日
计算机问题求解 – 论题3-15 - 线性规划 2017年2月20日
maximize X1 X2 subject to 问题1: 4x1 X2 ≤ 8 2x1 X2 ≤ 10 5x1 你能否利用左边 2x2 ≥ -2 X1,X2 ≥ 0 的式子和图解释: 222-2 目标函数、约束 条件、可行解、 =8 目标值、目标值 21+x10 x+x 的可行解、线性 规划问题的解、 5≥0 +=0 线性规划?
问题2.1: 为什么可行区域一定是凸的?这个性质有什么好处? 问题2.2: 如果目标函数系数均为正数,原点是一个可行解, 我们该如何寻找最优解? X 3≥0 为+=0
问题2.1: 为什么可行区域一定是凸的?这个性质有什么好处? 问题2.2: 如果目标函数系数均为正数,原点是一个可行解, 我们该如何寻找最优解?
问惠3 policy urban suburban rural 如何瘿邻下列语句: build roads -2 5 3 gun control 8 2 -5 Although we cannot easily graph farm subsidies 0 0 10 linear programs with more than two gasoline tax 10 0 -2 variables,the same intuition holds.If we have three variables,then each constraint corresponds to a half- space in three-dimensional space. The intersection of these half-spaces forms the feasible region. minimize x1+X2十 X3 十 X4 subject to -2x1+8x2+ 0x3+ 10x4 ≥ 50 5x1+2x2+0x3 0x4 100 3x1-5x2+10x3 2X4 25 X1,X2,X3,X4 0
Although we cannot easily graph linear programs with more than two variables, the same intuition holds. If we have three variables, then each constraint corresponds to a halfspace in three-dimensional space. The intersection of these half-spaces forms the feasible region
单形是什么?单形算法的基本 思路在哪里? x1+x2+X3>=1形成的半空间 x1+X2+x3=1形成的平面
x1+x2+x3=1形成的平面 x1+x2+x3>=1形成的半空间 单形是什么?单形算法的基本 思路在哪里?
问题4: 线性规划问题中的不等 式能不能用严格的大于 或小于?
线性规划问题的标准形式 maximize j=1 subject to ax≤bi for i=1,2,,m j=1 x≥0forj=1,2,..,n maximize cTx subject to Ax ≤b x≥0
线性规划问题的标准形式
minimize -2x1+3x2 subject to x1+x2 =7 1- 2x2 4 X1 ≥0 问题5: 为什么说这不是“标准形式
mizing a linear function subject to linear constraints,into standard form.A linear program might not be in standard form for any of four possible reasons: 1.The objective function might be a minimization rather than a maximization. 2.There might be variables without nonnegativity constraints. 3.There might be equality constraints,which have an equal sign rather than a less-than-or-equal-to sign. 4.There might be inequality constraints,but instead of having a less-than-or- equal-to sign,they have a greater-than-or-equal-to sign
minimize -2x1+3x2 maximize 2x1 3x2 subject to subject to x1+ X2 =7 x1+ X2 =7 x1-2x2 4 → x1-2x2 ≤4 x1 0. X1 ≥0 问题6: 如何将它转化为标准形式?这 两个线性规划“一样”吗?