linear and nonlinear scales
SAP2000® Linear and Nonlinear Static and Dynamic Analysis and Design of Three-Dimensional Structures
... the grids and spacing in the X, Y and Z direction Set the number of grid spaces to 10 for the X direction, and to for the Y and Z directions Type ft into the X direction spacing edit box and press ... loads only, and the deck will be loaded with a Dead Load = 10 pounds per square foot (psf) and a Live Load = 100 psf The Interface The top menu line contains all of the commands and options available ... Assign, Analyze, Display and Design These listed menus contain the commands that will be needed most often when using SAP2000, and many of the most frequently used commands are accessible as a...
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SAP2000® Linear and Nonlinear Static and Dynamic Analysis and Design of Three-Dimensional Structures GETTING STARTED doc
... nonlinear shell element, and geometric nonlinearity Analysis capabilities include static nonlinear analysis for material and geometric effects, including pushover analysis; nonlinear time-history ... a nonlinear link element (gaps, hooks, isolators, dampers, and multi -linear plasticity), a multi -linear plastic hinge for use in frame elements, a fiber hinge, a catenary cable element, a nonlinear ... and run (described in subsequent text) to specify how the load cases are to be applied (e.g., statically, dynamically, and so on) and how the structure is to be analyzed (e.g., linearly, nonlinearly,...
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gerald beresford whitham linear and nonlinear waves pure and applied mathematics 1974
... 517 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 ... s(t) and that xl and x2 are chosen so that x, >x2 Suppose p and q and their first derivatives are continuous in xx >x >s(t) and in s(t)>x> x2, and have finite limits as x—>s(t) from above and ... 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:...
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Báo cáo hóa học: " Linear and Nonlinear Oblivious Data Hiding" ppt
... Linear and Nonlinear Oblivious Data Hiding 2103 part, a novel data hiding algorithm is proposed, and its performance is analyzed and compared with existing schemes ... of the continuous segments, and the signaling has a pattern like XOXO as depicted in Figure 10 Signal points X and O have equal a priori probabilities Linear and Nonlinear Oblivious Data Hiding ... QIM scheme However, even under the same Linear and Nonlinear Oblivious Data Hiding O X O X O 2111 X O X O (a) (b) Figure 16: BER in (a) periodic signaling and (b) nonperiodic signaling 0.5 0.45...
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david g luenberger yinyu ye linear and nonlinear programming international series in operati docx
... three major parts: Linear Programming, Unconstrained Problems, and Constrained Problems The last two parts together comprise the subject of nonlinear programming Linear Programming Linear programming ... A linear programming problem is characterized, as the name implies, by linear functions of the unknowns; the objective is linear in the unknowns, and the constraints are linear equalities or linear ... PROGRAMS 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 linear inequalities...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 1 doc
... three major parts: Linear Programming, Unconstrained Problems, and Constrained Problems The last two parts together comprise the subject of nonlinear programming Linear Programming Linear programming ... A linear programming problem is characterized, as the name implies, by linear functions of the unknowns; the objective is linear in the unknowns, and the constraints are linear equalities or linear ... PROGRAMS 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 linear inequalities...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 2 ppsx
... understanding of the result The main link between the algebraic and geometric theories is the formal relation between basic feasible solutions of linear inequalities in standard form and extreme ... 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 ... solution Fundamental theorem of linear programming Given a linear program in standard form (11) where A is an m × n matrix of rank m, 2.4 The Fundamental Theorem of Linear Programming 21 i) if there...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 3 ppsx
... linear programs, however, and it is necessary to develop a means for determining one so that the simplex method can be initiated Interestingly (and fortunately), an auxiliary linear program and ... initially, a last row consisting of the ci ’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 in ... positive weights on a1 and a2 because b lies between them A basic feasible solution cannot be constructed with positive weights on a1 and a4 Suppose we start with a1 and a2 as the initial basis...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 4 doc
... 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 ... due to Bland [B19] For the state of the art in Simplex solvers see Bixby [B18] Chapter DUALITY Associated with every linear program, and intimately related to it, is a corresponding dual linear...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 5 docx
... 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 ... 12 and xi i = subject to 17 Given the linear programming problem in standard form (3) suppose a basis B and the corresponding (not necessarily feasible) primal and dual basic solutions x and ... that is feasible for the dual and that x and y = is feasible (and of course optimal) for the associated restricted primal Then x and are optimal for the original primal and dual programs, respectively...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 6 pptx
... chapters Not only have nonlinear methods improved linear programming, but interiorpoint 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 them ... for linear programming is to use nonlinear programming techniques of analysis and methodology The analysis is often based on differentiation of the functions defining the problem Traditional linear...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 7 pps
... Tutuncu [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 ... Computation and complexity models were developed by a number of scientists; see, e.g., Cook [C5], Hartmanis and Stearns [H5] and Papadimitriou and Steiglitz [P2] for the bit complexity models and Blum ... 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...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 8 pdf
... intermediate level, and power is purchased directly only for peak demand periods The requirements are satisfied as shown in Fig 7.2(b), where x1 and x2 denote the capacities of the nuclear and coal-fired ... node and ci is the maximal flow that can be sent from the source to node i through the path created by the previous labeling and scanning The complete procedure is this: Step Set all xij = and ... divide the nodes arbitrarily into two sets S and S such that the ¯ ¯ source node is in S and the sink is in S The set of arcs from S to S is a cut and is ¯ denoted (S S) The capacity of the cut...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 9 ppsx
... 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 ... 13 Let rk k=0 and ck k=0 be sequences of real numbers Suppose rk → average linearly and that there are constants c > and C such that c ck C for all k Show that ck rk → average linearly 14 Prove ... solution set and let A be an algorithm on X A continuous real-valued function Z on X is said to be a descent function for and A if it satisfies i) if x ii) if x ∈ and y ∈ A x , then Z y < Z x and y...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 1 Part 10 pot
... xk − f ∗ Clearly a/ A < and hence there is linear convergence Notice if that in fact is chosen very close to and is chosen very close to 1, then the stopping condition demands that the be restricted ... point x4 is calculated from the quadratic fit in the standard way and f x4 is measured Assuming (as in the figure) that x2 < x4 < x3 , and accounting for the unimodal nature of f , there are ... be replaced by f x4 , and by construction, and the assumption that f is unimodal, it will replace a strictly larger value Of course, at x∗ = x∗ x∗ x∗ we have A x∗ = x∗ and hence Z A x∗ = Z x∗...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 1 pot
... practice Newton’s Method and Logarithms Interior point methods of linear and nonlinear programming use barrier functions, which usually are based on the logarithm For linear programming especially, ... Boyd and Vandenberghe [B23] The numerical problem considered in the example is a standard one See Faddeev and Faddeeva [F1] 8.8 For good reviews of modern Newton methods, see Fletcher [F9] and ... = xk − k gk where 1− and k k k 1+ k minimizes f xk − gk over a) Find the convergence rate of the algorithm in terms of a and A, the smallest and largest eigenvalues of Q, and the tolerance Hint:...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 2 ppt
... standard steepest descent step from xk , and then xk+1 is taken to be the minimum point on the line connecting xk−1 and yk The process is continued for n steps and then restarted with a standard ... Daniel [D1] and Faddeev and Faddeeva [F1] 9.5 The partial conjugate gradient method presented here is identical to the so-called s-step gradient method See Faddeev and Faddeeva [F1] and Forsythe ... Faddeev and Faddeeva [F1], and Luenberger [L8] The result stated in Exercise is due to Hestenes and Stiefel [H10] Exercise is due to Powell [P6] For the solution to Exercise 10, see Faddeev and Faddeeva...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 3 pot
... DESCENT AND NEWTON’S METHOD In this section we digress from the study of quasi-Newton methods, and again expand our collection of basic principles We present a combination of steepest descent and ... formula, and for this reason it is now generally preferred It can be noted that both the DFP and the BFGS updates have symmetric rank two corrections that are constructed from the vectors pk and Hk ... the solution, and hence convergence will be superlinear Unfortunately, while the methods are certainly excellent, their convergence characteristics require more careful analysis, and this will...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 4 pps
... many examples of nonlinear programming in industrial operations and business decision making Many of these are nonlinear versions of the kinds of examples that were discussed in the linear programming ... general nonlinear programming problems of the form minimize subject to fx h1 x = h2 x = g1 x g2 x 0 hm x = gp x x ∈ ⊂ En (1) m and gj j = p where m n and the functions f , hi i = are continuous, and ... Larger, more complex, nonlinear programming problems arise frequently in modern applied analysis in a wide variety of disciplines Indeed, within the past few decades nonlinear programming has...
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David G. Luenberger, Yinyu Ye - Linear and Nonlinear Programming International Series Episode 2 Part 5 potx
... the demand for the three sizes are independent and the demand for each size is uniformly distributed between zero and three thousand pairs He wishes to allocate his shoe budget of four thousand ... the sets A and B in E m+1 as A= r y r≥ B= r y r ≤ f∗ y = y y∈C A is the epigraph of (see Section 7.6) and B is the vertical line extending below f ∗ and aligned with the origin Both A and B are ... The sets A and B and the separating hyperplane 11.9 Zero-Order Conditions and Lagrange Multipliers 349 Geometrically, if s = the hyperplane would be vertical We wish to show that s = 0, and it is...
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