mixed integer nonlinear programming

... PROGRAMMING BASED ON LECTURES GIVEN AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY CAMBRIDGE, MASS DIMITRI P. BERTSEKAS These lecture slides are based on the book: Nonlinear Programming, ” Athena Scientific, by ... NONLINEAR PROGRAMMING LECTURE 1: INTRODUCTION LECTURE OUTLINE ã Nonlinear Programming ã Application Contexts ã Characterizatio...

Ngày tải lên: 26/10/2013, 17:15

... 342–350, Suntec, Singapore, 2-7 August 2009. c 2009 ACL and AFNLP Concise Integer Linear Programming Formulations for Dependency Parsing Andr ´ e F. T. Martins ∗† Noah A. Smith ∗ Eric P. Xing ∗ ∗ School ... solution for many problems. Their per- formance depends on the dimensions and degree of sparsity of the constraint matrix A. Riedel and Clarke (2006) proposed an ILP for-...

Ngày tải lên: 20/02/2014, 07:20

... Grammatical Role Labeling with Integer Linear Programming Manfred Klenner Institute of Computational Linguistics University ... Zurich klenner@cl.unizh.ch Abstract In this paper, we present a formalization of grammatical role labeling within the framework of Integer Linear Programming (ILP). We focus on the integration of sub- categorization ... only. With grammatical rol...

Ngày tải lên: 17/03/2014, 22:20

... a change in speaker has occurred between the current and previous contribution. 4.3 Constraints using Integer Linear Programming We formulate our constraints using Integer Linear Programming ... 1018–1026, Portland, Oregon, June 19-24, 2011. c 2011 Association for Computational Linguistics Recognizing Authority in Dialogue with an Integer Linear Programming Con...

Ngày tải lên: 23/03/2014, 16:20

... 2 introduces first the elementary notions of mixed- integer linear optimization and focuses subsequently on the theoretical and algorithmic developments in mixed- integer nonlinear optimization. ... and there exist nonlinear terms in the objective function and constraints, then (1.1) is a mixed- integer nonlinear programming MINLP problem. The...

Ngày tải lên: 01/04/2014, 11:35

... of mixed- integer optimal control problems. . . . 631 Sebastian Sager List of Hot Topics participants 671 FOREWORD This IMA Volume in Mathematics and its Applications MIXED INTEGER NONLINEAR PROGRAMMING contains ... n-fold integer programming (S. Onn) is an overview of the theory of n-fold integer programming, which enables the polynomial-time solution of fundamental linear...

Ngày tải lên: 30/05/2014, 00:33

... approximate optimal solutions and a generalized augmented La- grangian in nonlinear programming, establish dual function and dual problem based on the generalized augmented Lagrangian, obtain approximate ... function and dual problem based on the generalized aug mented Lagrangian, obtain approximate KKT necessary optimality condition of the generalized...

Ngày tải lên: 22/06/2014, 18:20

... divided into three major parts: Linear Programming, Unconstrained Problems, and Constrained Problems. The last two parts together comprise the subject of nonlinear programming. Linear Programming Linear ... are introduced for each time period. In particular, let x i denote the level of stock in the warehouse at the beginning of Linear and Nonlinear Programming Thir...

Ngày tải lên: 27/06/2014, 17:20

... Mathematics and its Applications MIXED INTEGER NONLINEAR PROGRAMMING contains expository and research papers based on a highly successful IMA Hot Topics Workshop Mixed- Integer Nonlinear Optimization: ... VIII: Complexity On the complexity of nonlinear mixed- integer optimization . . . . . . . . . . 533 Matthias Kăoppe Theory and applications of n -fold integer programming...

Ngày tải lên: 01/08/2014, 16:47

... Sensitivity 339 11 .8. Inequality Constraints 3 41 11. 9. Zero-Order Conditions and Lagrange Multipliers 346 11 .10 . Summary 353 11 .11 . Exercises 354 Chapter 12 . Primal Methods 359 12 .1. Advantage of ... 3 21 11. 2. Tangent Plane 323 11 .3. First-Order Necessary Conditions (Equality Constraints) 326 11 .4. Examples 327 11 .5. Second-Order Conditions 333 11 .6. Eigenvalues in...

Ngày tải lên: 06/08/2014, 15:20

... equations x 1 + x 2 −x 3 = 5 2x 1 −3x 2 +x 3 = 3 −x 1 +2x 2 −x 3 = 1 To obtain an original basis, we form the augmented tableau e 1 e 2 e 3 a 1 a 2 a 3 b 10 0 1 1 15 010 2 313 0 01 12 1 1 and replace e 1 by ... obtain x 1 x 2 x 3 x 4 x 5 x 6 3/ 51/ 5 010 2/ 518 /5 2/ 5 1/ 50 01 3/57/5 1/ 53/ 510 0  1/ 5 1/ 5 Continuing, there results x 1 x 2 x 3...

Ngày tải lên: 06/08/2014, 15:20

... sake of safety. 54 Chapter 3 The Simplex Method x 2 x 3 x 4 x 5 x 6 x 7 b 1 10 1 10 1 12 10 11 2 1 − 210 20−2 Second tableau—phase I 01 11 01 3 12 10 11 2 00 00 11 0 Final tableau—phase I Now ... problem x 2 x 3 x 4 x 5 b 01 11 3 12 10 2 c T 23 11 14 Initial tableau—phase II Transforming the last row appropriately we proceed with: 01 11 3 1 2 10 2 0 −220− 21 Fi...

Ngày tải lên: 06/08/2014, 15:20

... and new  as follows. Variable B 1 Value s 1 1 10 012  2 0 1/ 2 0 1 1/2 0  1 0 1/ 2 1 1 1/ 2 1  2 0 0 0 1 1/2 0 s 1 10−2 −20  2 0 1/ 2 0 1 1/2  3 0 1/ 2 1 1 1/ 2  3 0 0 011  T =  0 4 ... −3000 1 1 1/ 2 1/ 2 0 2 10 1 11 2 30 12 0 8 3/2 1 0 1 1/ 21 10 1 11 2 20 01 110 The optimal solution is x 1 =0, x 2 =1, x 3 =2. The corresponding dual progr...

Ngày tải lên: 06/08/2014, 15:20

... row. a 1 a 2 a 3 ··b 1 12 10 3 213 0 15 −3 −2 50 0−8 1/ 203/2 ··· Second tableau Minimizing the new associated restricted primal by pivoting as indicated we obtain a 1 a 2 a 3 ··b 11 210 3 10 1 11 2 10 12 0−2 1/ 203/2 ... tableau: a 1 a 2 a 3 ··b 011 2 11 10 1 11 2 00 011 0 0 01 ·· Final tableau ∗ 4.7 Reduction of Linear Inequalities 10 1 By subtracting the second equati...

Ngày tải lên: 06/08/2014, 15:20

... +1 =  1+ 1 m 2 1  m 1 /2  1 1 m +1  < exp  1 2m +1 − 1 m +1  =exp  − 1 2m +1   Convergence The ellipsoid method is initiated by selecting y 0 and R such that condition (A1) ... S 1 we have d x +S 1 Xd s =S 1 1−x Then, premultiplying by A and using Ad x =0, we have AS 1 Xd s =AS 1 1−Ax =AS 1 1−b Using d s =−A T d y we have AS 1 XA T...

Ngày tải lên: 06/08/2014, 15:20