PPT-SOLVING LINEAR PROGRAMS Dr. Ron Lembke

Solving LPs Need a more formal method How to find points to solve for A picture is worth a thousand words Standard Form Linear programs are written the following way Max 20 S 25 T . e Ax where is vector is a linear function of ie By where is then is a linear function of and By BA so matrix multiplication corresponds to composition of linear functions ie linear functions of linear functions of some variables Linear Equations Let be some operator and a vector If does not change the direction of the vector is an eigenvector of the operator satisfying the equation 1 where is a real or complex number the eigenvalue corresponding to the eigenvector Thus the operator will o =0 and a = 2a - an-2 = 3n Initial conditionsRecurrence relation Solution = 1a = 6a = 10 = a + 2an-2 = a + 2a 3Linear recurrencesLinear recurrences1.Linear homogeneous recurrences2.Linear non-homogene Recurrence Relations. ICS 6D. Sandy . Irani. Recurrence Relations. to Define a Sequence. g. 0 . = 1. For n . 2, . g. n. = 2 g. n-1. + 1. A . closed form solution . for a recurrence relation, gives the n. Homogeneous Linear . Recursion. CK Cheng. May 5, 2011. 2. 3. Analysis . 3.1 Introduction . 3.2 Homogeneous Linear Recursion. 3.3 Pigeonhole Principle. 3.4 Inclusion-Exclusion Principle . 3. 3.1 Introduction . Reals. Dana . Moshkovitz. , MIT. Joint work with . Subhash. . Khot. , NYU. We propose an approach for proving the . unique games conjecture . by studying the hardness of approximately solving . real. Dr. Ron Lembke. Formulating in Excel. Write the LP out on paper, with all constraints and the objective function.. Decide on cells to represent variables.. Enter coefficients of each variable in each constraint in a block of cells.. Some of these recurrence relations can be solved using iteration or some other ad hoc technique. . However, one important class of recurrence relations can be explicitly solved in a systematic way. These are recurrence relations that express the terms of a sequence as linear combinations of previous terms.. Introduction to Linear Programming. Introduction. Linear programming. Programming means planning. Model contains linear mathematical functions . An application of linear programming. Allocating limited resources among competing activities in the best possible way. Equations Using Algebra Tiles . Objectives. Solving Equations Involving the Distributive Property. Solving Multi-Step Equations. Solving Equations. The development of the equation solving model is based on two ideas.. by . Graphing. Key Terms:. A system of two linear Equations – in ____ variables x and y, consist of two linear equations. . Solution – consist of an order pair_____ .. Two Types:. Consistent – At least one Solution. Section . 3.2a. 8/10/2012 8:57 PM. 3.2a - Solving Systems through Substitution. 1. Steps in Substitution. SOLVE. . for one equation into one variable. REPLACE. . one equation into other equation. SUBSTITUTE. How would we formulate this as a linear program?. Announcements. Assignments:. HW4 (written). Due Tue 2/12, 10 pm. P2: Optimization. Released after lecture. Due Thu 2/21, 10 pm. Midterm 1 Exam. Mon 2/18, in class. Siu. A. Chin. Texas A&M University. Castellon, Sept. 6, 2010. Forward. algorithms, with all positive time steps for solve time-irreversible equations with a diffusion kernel beyond the second-order. .