linear and nonlinear system

... EFFORT AND EXPENSE HAVE GONE INTO THE DEVELOPMENT AND DOCUMENTATION OF SAP2000. THE PROGRAM HAS BEEN THOROUGHLY TESTED AND USED. IN USING THE PROGRAM, HOWEVER, THE USER ACCEPTS AND UNDERSTANDS ... number and spacing of the grid lines. Select the Grid Only button, and the form shown in Figure 4 will display. C. The New Coord/Grid System form is used to specify the grids and spacing ... spacing in the X, Y and Z direction. Set the number of grid spaces to 10 for the X direction, and to 1 for the Y and Z directions. Type 6 ft into the X direction spacing edit box and press the Enter...

Ngày tải lên: 06/09/2012, 15:56

... Dimensions and tolerances – merge, selection, and snap tolerances; font sizes; zoom increment; and others  Design codes and their parameters  Colors of objects and results for display and printing ... locations, nonlinear properties, line springs and masses, automated meshing parameters, and more  Assigning properties to area objects, including section properties, local coordinate systems, ... Design, Display, and Output operations. To select, enable the Select Mode using the Draw menu > Set Select Mode command, or by choosing any command from the Select menu. Draw Mode and Select...

Ngày tải lên: 01/04/2014, 03:20

... 15.4 Nonlinear Group Velocity, Group Splitting, Shocks, 519 15.5 Higher Order Dispersive Effects, 522 15.6 Fourier Analysis and Nonlinear Interactions, 527 16 Applications of the Nonlinear ... at x = s(t) and that x l and x 2 are chosen so that x, >x 2 . Suppose p and q and their first derivatives are continuous in x x >x >s(t) and in s(t)>x> x 2 , and have finite ... fundamental ideas in nonlinear hyperbolic waves. The most outstanding new phenomenon of the nonlinear theory is the appearance of shock waves, which are abrupt jumps in pressure, density, and velocity:...

Ngày tải lên: 12/06/2014, 16:26

... Newark, NJ, between March 2000 and August 2002. His re- search interests include sensor/ad hoc networks, cryptography, data hiding, and data compression. Linear and Nonlinear Oblivious Data Hiding ... further studies establish that the Linear and Nonlinear Oblivious Data Hiding 2103 part, a novel data hiding algorithm is proposed, and its per- formance is analyzed and compared with existing schemes. The ... Corporation Linear and Nonlinear Oblivious Data Hiding Litao Gang InfoDesk, Inc., 660 White Plains Road, Tarrytown, NY 10591, USA Email: lxg8906@njit.edu Ali N. Akansu Department of Electrical and Computer...

Ngày tải lên: 23/06/2014, 01:20

... major parts: Linear Programming, Unconstrained Problems, and Constrained Problems. The last two parts together comprise the subject of nonlinear programming. Linear Programming Linear programming ... the system of linear equations that defines the constraints and the basic feasible solutions of the system. This approach, which focuses on individual variables and their relation to the system, ... unknowns and constraints; intermediate-scale problems having from about five to a hundred or a thousand variables; and large-scale problems having perhaps thousands or even millions of variables and...

Ngày tải lên: 27/06/2014, 17:20

... PROPERTIES OF LINEAR PROGRAMS 2.1 INTRODUCTION A linear program (LP) is an optimization problem in which the objective function is linear in the unknowns and the constraints consist of linear equalities and ... major parts: Linear Programming, Unconstrained Problems, and Constrained Problems. The last two parts together comprise the subject of nonlinear programming. Linear Programming Linear programming ... Descent 233 Linear and Nonlinear Programming Third Edition David G. Luenberger Stanford University Yinyu Ye Stanford University 123 PART I LINEAR PROGRAMMING 1.4 Iterative Algorithms and Convergence...

Ngày tải lên: 06/08/2014, 15:20

... the system of linear equations that defines the constraints and the basic feasible solutions of the system. This approach, which focuses on individual variables and their relation to the system, ... Bazaraa, Jarvis, and H. F. Sherali [B6], Bertsimas and Tsitsiklis [B13], Cottle, [C6], Dantzig and Thapa [D9, D10], Nash and Sofer [N1], Saigal [S1], and Vanderbei [V3] 2.5 An excellent discussion of ... or less standard approach to linear programming as presented in, for example, Dantzig [D6], Hadley [H1], Gass [G4], Simonnard [S6], Murty [M11], and Gale [G2]. Also see Bazaraa, Jarvis, and H. F....

Ngày tải lên: 06/08/2014, 15:20

... matrix and U is an upper triangular matrix. † Then each of the linear systems (35) can be solved by solving two triangular systems. Since solving in this fashion is simple, knowledge of L and U ... efficiency and numerical stability, however, this pivoting procedure is not as effective as the method of Gaussian elimination for general systems of linear equations (see Appendix C), and it therefore ... initially, a last row consisting of the c i ’s and a right-hand side of zero can be appended to the standard array to represent this additional equation. Using standard pivot operations, the elements...

Ngày tải lên: 06/08/2014, 15:20

... artificial basis technique; Dantzig, Orden and Wolfe [D8], Orchard-Hays [O1], and Dantzig [D4] for the revised simplex method; and Charnes and Lemke [C3] and Dantzig [D5] for upper bounds. The synthetic ... several fixed origins and destinations so as to minimize transportation cost while satisfying demand. Referring to (6) and (7) of Chapter 2, the problem is in standard form, and hence the asymmetric ... Duality feasible for (3) and hence r/t 0 =z 0 −c T x 0; which means r 0.Ifw =−Ax 0 =0 with x 0  0 and c T x 0 =−1, and if x is any feasible solution to (3), then x+x 0 is feasible for any   0 and gives...

Ngày tải lên: 06/08/2014, 15:20

... lines of (25) represent a system of linear inequalities in standard form with one less variable and one less equation than the original system. The last equation is a simple linear equation from which ... x 3 =0. ∗ 4.7 REDUCTION OF LINEAR INEQUALITIES Linear programming is in part the study of linear inequalities, and each progressive stage of linear programming theory adds to our understanding of this important fundamental ... for solving such systems. Duality theory provides additional insight and additional techniques for dealing with linear inequalities. Consider a system of linear inequalities in standard form Ax...

Ngày tải lên: 06/08/2014, 15:20

... chapters. Not only have nonlinear methods improved linear programming, but interior- point methods for linear programming have been extended to provide new approaches to nonlinear programming. This ... intended to show how this merger of linear and nonlinear programming produces elegant and effective methods. These ideas take an especially pleasing form when applied to linear programming. Study of ... complexity bound and is often used in linear programming software packages. The algorithm is based on the construction of a homogeneous and self-dual linear program related to (LP) and (LD) (see...

Ngày tải lên: 06/08/2014, 15:20

... [T11], and others. The homogeneous and self-dual embedding method can be found in Ye et al. [Y2], Luo et al. [L18], Andersen and Ye [A5], and many others. It is also implemented in most linear programming ... right corner element, and it gives u 4 =2. Then, from the equation 4 =2 + 4 ,  4 is found to be 2. Next, u 3 and u 2 are determined, then  3 and  2 , and finally u 1 and  1 . The result is ... Tanabe [T2] and Todd and Ye [T5]. The primal-dual potential reduction algorithm was developed by Ye [Y1], Freund [F18], Kojima, Mizuno and Yoshise [K7], Goldfarb and Xiao [G11], Gonzaga and Todd...

Ngày tải lên: 06/08/2014, 15:20

... Transportation and Network Flow Problems C = ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ 03364 30548 35025 64205 48550 ⎤ ⎥ ⎥ ⎥ ⎥ ⎦  In this system points 1 and 2 are net suppliers, points 4 and 5 are net demanders, and point 3 ... intermediate level, and power is purchased directly only for peak demand periods. The requirements are satisfied as shown in Fig. 7.2(b), where x 1 and x 2 denote the capacities of the nuclear and coal-fired ... stone method. 6.5 The assignment problem has a long and interesting history. The important fact that the integer problem is solved by a standard linear programming problem follows from a theorem of...

Ngày tải lên: 06/08/2014, 15:20

... define corresponding notions of average linear and average superlinear convergence. Although the above array of definitions can be further embellished and expanded, it is quite adequate for our purposes. ... r k   k=0 and c k   k=0 be sequences of real numbers. Suppose r k →0 average linearly and that there are constants c>0 and C such that c  c k  C for all k. Show that c k r k →0 average linearly. 14. ... 7.7. Proposition. Let A X→Y and B Y →Z be point-to-set mappings. Suppose A is closed at x and B is closed on A(x). Suppose also that if x k → x and 7.4 Convex and Concave Functions 193 f x convex (a) f x nonconvex (c) f x convex (b) Fig....

Ngày tải lên: 06/08/2014, 15:20

... −f ∗  Clearly 2a/A < 1 and hence there is linear convergence. Notice if that in fact  is chosen very close to .5 and  is chosen very close to 1, then the stopping condition demands that the  be ... available, fast convergence, and a guarantee of global convergence. 8.4 CLOSEDNESS OF LINE SEARCH ALGORITHMS Since searching along a line for a minimum point is a component part of most nonlinear programming ... Exercise 2) gx k−1 x k  = g   k  (14) and gx k−1 x k x ∗  = 1 2 g  k (15) where  k and  k are convex combinations of x k , x k−1 and x k , x k−1 , x ∗ , respec- tively. Thus x k+1 −x ∗ = g   k  2g   k  x k −x ∗ x k−1 −x ∗ ...

Ngày tải lên: 06/08/2014, 15:20

Ngày tải lên: 06/08/2014, 15:20

Ngày tải lên: 06/08/2014, 15:20

Ngày tải lên: 06/08/2014, 15:20

Ngày tải lên: 06/08/2014, 15:20

Ngày tải lên: 06/08/2014, 15:20