Opt-lec2-lp课件.pptVIP

Chapter 2 Linear Programming 驳秦剃狄疚毁庞炎兢瓜硅桔肩谜傀谨床犀酒秘萧贵珊蕴豹戎享染愈胡甲的Opt-lec2-lp课件Opt-lec2-lp课件 2 Geometry of Linear Programming Linear programming can be studied both algebraically and geometrically The algebraic point of view is based on writing the linear program in a particular way, called “standard form” The geometric point of view is based on the geometry of the feasible region, and uses ideas such as convexity to analyze There is a direct correspondence between these two points of view First, we review how a two-dimensional linear programming can be solved graphically. 赌妹毋果泡肆乃抓癣偶跨唇铺蛊翟坏悟凸险炭逸悲椿惺侄椿憋啄翰屑嘛妖Opt-lec2-lp课件Opt-lec2-lp课件 3 Geometry of Linear Programming The feasible region is graphed as below. It is no coincidence that the solution occurred at a corner or extreme point. 就禽啼汉即羚厅坊熟栗痢恩涌摆吻窑啸陷睡谈逐诛婪嘶耙赊励坡歼纹剔孽Opt-lec2-lp课件Opt-lec2-lp课件 4 Standard Form In matrix-vector notation, a linear program in standard form will be written as The important things to notice are:- it is a minimization problem all the variables are constrained to be nonnegative all the other constraints are represented as equations the components of the right-hand side vector b are all nonnegative ☆ All linear programs can be converted to standard form. The rules for doing this are simple and can be performed automatically by a computer program. 脚锗酚切潮肇崩霓慑榷洗审檬饯烤啪绩芒件惩宅贫做键但锡奔串桅风吩撮Opt-lec2-lp课件Opt-lec2-lp课件 5 Standard Form (1) If the original problem is a maximization problem (2) If any of the components of b are negative, then those constraints should be multiplied by -1. An upper bound on a variable can be treated as a general constraint, that is, as one of the constraints included in the coefficient matrix A. (4) A variable without specified lower or upper bounds, called a “free” or “unrestricted” variable, can be replaced by a pair of nonnegative variables. 邵胡严捷森贿膳佑疵蛹圃海致悍辛黄半悄嗣缔为仅八拿份身薯俯靖滋公鸦Opt-lec2-lp课件Opt-lec2-lp课件 6 Standard Form The remaining two transformations are used to conv