A.L. Peressini, F.E. Sullivan, K.J. Uhl, The Mathematics of Nonlinear Programming, Springer, New York, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... a nodding acquaintance with the theory of NPcompleteness, for which standard references include Garey and Johnson [77] and Papadimitriou [141] and with the basics of linear and nonlinear programming; accessible introductions to these two fields are given by Chvatal [34] and Peressini et al. [145], respectively. We assume no knowledge of game theory; however, some of our definitions and results may appear more natural to the reader familiar with basic game theoretic concepts. Standard introductions to game theory include Fudenberg and Tirole [75] Osbourne and Rubinstein [139] and Owen ....

....function for each edge e, with marginal cost A function f defined on a convex subset S of is convex if f(#x (1 #)y) #f(x) 1 #)f(y) for all x, y S and # [0, 1] Some authors call such functions weakly convex. For a formal derivation via the Karush Kuhn Tucker Theorem [145], see [17, 50] 23 functions # # defined as above. Then a flow f feasible for (G, r, #) is optimal if and only if it is at Nash equilibrium for the instance (G, r, # # ) Remark 2.3.3 We will typically denote a minimum latency flow for an instance by f # . The marginal cost functions are denoted ....

A. L. Peressini, F. E. Sullivan, and J. J. Uhl. The Mathematics of Nonlinear Programming. Springer-Verlag, 1988.

....and has been extensively studied ever since (see [27] for many more references) Beckmann et al. 4] showed that marginal cost taxes produce a minimum latency routing of tra#c when #(a) 1 for all users a. This is accomplished by a simple application of the Karush Kuhn Tucker theorem (see e.g. [23]) to an appropriate convex program. Marginal cost pricing has also been studied with heterogeneous network users; unfortunately, extending the techniques of [4] to this more general setting requires users with di#erent # values to pay di#erent taxes on the same edge [11, 30] This solution is ....

A. L. Peressini, F. E. Sullivan, and J. J. Uhl. The Mathematics of Nonlinear Programming. Springer-Verlag, 1988.

....and has been extensively studied ever since (see [25] for many more references) Beckmann et al. 4] showed that marginal cost taxes produce a minimum latency routing of traffic when #(a) 1 for all users a. This is accomplished by a simple application of the Karush Kuhn Tucker theorem (see e.g. [21]) to an appropriate convex program. Marginal cost pricing has also been studied with heterogeneous network users; unfortunately, extending the techniques of [4] to this more general setting requires users with different # values to pay different taxes on the same edge [10, 28] This solution is ....

A. L. Peressini, F. E. Sullivan, and J. J. Uhl. The Mathematics of Nonlinear Programming. SpringerVerlag, 1988.

.... Cheeseman, 1986] The robotics community has developed algorithms to solve a network of spatial relations [Durrant Whyte, 1987, Durrant Whyte, 1988a, Durrant Whyte, 1988b, Moutarlier and Chatila, 1989] Techniques from multidimensional scaling [Borg and Groenen, 1997] and nonlinear programming [Peressini et al. 1988] can also be used. 10 10 10 20 20 10 10 10 20 20 9 5 2 13 6 7 8 10 20 20 10 10 4,11 (b) c) a) d) Figure 19: a) The robot goes around the block visiting distinctive states ds# to ds## in the order suggested by the figure. Distinctive state ds## is observed at the same ....

Antony L. Peressini, Francis E. Sullivan, and K. Jerry Uhl. The mathematics of nonlinear programming. Springer-Verlag, New York, 1988.

.... Cheeseman, 1986] The robotics community has developed algorithms to solve a network of spatial relations [Durrant Whyte, 1987, Durrant Whyte, 1988a, Durrant Whyte, 1988b, Moutarlier and Chatila, 1989] Techniques from multidimensional scaling [Borg and Groenen, 1997] and nonlinear programming [Peressini et al. 1988] can also be used. The shortest path with respect to the number of edges in the path. The heuristic of choosing the shortest path assumes that the fewer places whose location must be determined, the more accurately their locations can be determined. 103 Next we show an algorithm to create a two ....

Antony L. Peressini, Francis E. Sullivan, and K. Jerry Uhl. The mathematics of nonlinear programming. Springer-Verlag, New York, 1988.

.... Cheeseman, 1986] The robotics community has developed algorithms to solve a network of spatial relations [Durrant Whyte, 1987, Durrant Whyte, 1988a, Durrant Whyte, 1988b, Moutarlier and Chatila, 1989] Techniques from multidimensional scaling [Borg and Groenen, 1997] and nonlinear programming [Peressini et al. 1988] can also be used. DRAFT November 13, 2001 35 10 10 10 20 20 10 10 10 20 20 9 5 2 13 6 7 8 10 20 20 10 10 10 4,11 (b) c) a) d) Figure 19: a) The robot goes around the block visiting distinctive states ds# to ds## in the order suggested by the figure. Distinctive ....

Antony L. Peressini, Francis E. Sullivan, and K. Jerry Uhl. The mathematics of nonlinear programming. Springer-Verlag, New York, 1988.

....condition should be necessary and sufficient for a flow to be globally optimal. The following lemma formalizes the preceding discussion. Letting c # P (f) # e#P c # e (f e ) where we are assuming differentiability for simplicity only) we may apply the Karush Kuhn Tucker Theorem (see, e.g. [25]) to a convex program of the form (NLP ) to derive the following characterization of optimal flows (see the full version [28] for details) Lemma 2.4 A flow f is optimal for a convex program of the form (NLP ) if and only if for every i # 1, k and P 1 , P 2 # P i with fP1 0, c # ....

A. L. Peressini, F. E. Sullivan, and J. J. Uhl. The Mathematics of Nonlinear Programming. Springer-Verlag, 1988.

....I 2 , # #g I K # T (35) # h R # # # #h R 1 , # #h R 2 , # #h R K # T (36) # h I # # # #h I 1 , # #h I 2 , # #h I K # T (37) Since Eqs. 29) 33) are nonlinear simultaneous equations, they can be solved using the iterative method; Newton s method[16] is used in this work. To apply Newton s method to the solution of Eqs. 29) 33) we define the Hessian matrix of L, the matrix of all the second partial derivatives of L, as the following block matrix form: H# # # # # # H g R ,g R H g R ,g I H g R ,h R H g R ,h I H g R ,# H g ....

....H given by Eqs. 38) and (40) 54) we can apply Newton s method to the solution of Eqs. 29) 33) i.e. col[# g R ,# g I ,# h R ,# h I ,# # ]L = 0, 0] T , where col[ denotes the column vector. In this method, we obtain the weight vectors of element in the (i 1) th step as [16] # g R , g I , h R , h I , # # T i 1 = # g R , g I , h R , h I , # # T i # H 1 i col # # g R , # g I , # h R , # h I , # # # L i , 55) where the subscript i is used to express the value of the i th step in the iterations explicitly, and # (0 ....

A.L. Peressini, F.E. Sullivan and J.J. Uhl, Jr., "The Mathematics of Nonlinear Programming," Springer-Verlag, New York, 1988.

....savings over conventional DSP systems in the context of frequency division multiplexed (FDM) communications without incurring any performance loss. In section 2, we review our past work in using AEC for ANT. In section 3, we derive the energy optimum AEC by using the Lagrange multiplier method [4]. Simulation results are presented and evaluated in section 4. 2. Algorithmic Noise Tolerance (ANT) for LowPower DSP In this section, we present the VOS and ANT concepts and describe the proposed AEC technique for designing lowpower DSP systems. 2.1. Energy savings via VOS Dedicated DSP ....

....the energy optimization problem for AEC can be written as minimize: b#B N EAEC (b) subject to: # e 2 # # 2 n,design # n 2 , 17) where EAEC (b) # e 2 , # n 2 and # 2 n,design are given by (16) 13) 7) and (8) respectively. Employing the Lagrange multiplier method [4], we obtain the solution b # = b # 0 , b # 1 , b # N 1 # B N of (17) as b # j = # 1 if EF,j w j 2 #x 2 # # , 0 if EF,j w j 2 #x 2 # # # , 18) where # # is the solution of sensitivity vector of the Lagrange multiplier. This gives the energy optimum length N opt c of ....

A. L. Peressini, F. E. Sullivan and J. J. Uhl, Jr., The Mathematics of Nonlinear Programming, SpringerVerlag, 1988.

....13 T 1 ( 1 fi fi ) i Gamma1) n Gamma1) fiC i = T i 1 Gamma T i = T 1 ff i Gamma1 (ff Gamma 1) and hence C i =T i = 1 fi (ff Gamma 1) i n Gamma 1 is a general solution to this program. Checking the result we see that C i 0, T i 0 for all i, so we have a feasible solution [11]. Therefore, U = n X i=1 C i =T i 1 fi ( n Gamma 1) 1 fi fi ) 1= n Gamma1) Gamma 1) 1 Gamma 1 fi ) if fi 1: Case 2. Assume that task n Gamma1 makes two requests in the time period [0; T n ] Then the results of Lemma 3.4 and the equality arguments from Case 1 yield the ....

A. L. Peressini, F. E. Sullivan, J. J. Uhl, The Mathematics of Nonlinear Programming, New York: Springer Verlag, 1988. DRAFT - Burst Processing 21

....n i=1 kp i Gamma pk is minimized. The point p is then the center of the smallest enclosing ball. The following lemma shows that this problem can be written in the form of QP. Its proof is omitted here it follows from the Karush KuhnTucker optimality conditions for convex optimization problems [12]. Lemma 5.1. For an n point set P = fp1 ; png, define the d Theta n matrix C : p1 ; pn) consider the quadratic programming problem (MB 0 ) minimize x T C T Cx Gamma P n i=1 p T i p i x i subject to P n i=1 x i = 1; x 0: 5) and let x 1 ; x n be its ....

A. L. Peressini, F. E. Sullivan, and J. J. Uhl. The Mathematics of Nonlinear Programming. Undergraduate Texts in Mathematics. Springer-Verlag, 1988.

....Eq. 20) is a problem of nonlinear minimization, it can be minimized using the iterative method. To express the value of i th step in the iterations explicitly, the weight vectors of element g and h are rewritten as g i and h i , respectively. As for an iterative method, the Gauss Newton method[18] is used. The weight vectors of element in the (i 1) th step are given as # g i 1 , h i 1 # T = # g i , h i # T # (WJ i ) We i , 23) where superscript denotes the pseudo inverse matrix and # (0 # = 1) is the step size parameter for iterations. J i is a Jacobian matrix ....

A.L. Peressini, F.E. Sullivan and J.J. Uhl, Jr., "The Mathematics of Nonlinear Programming," Springer-Verlag, New York, 1988.

....in suggesting methods which converge from a wider set of initial guesses. Simply using the convexity of V b we have that, while a full Newton step may give divergence, the Newton direction is a descent direction for V b so an appropriate partial Newton step can be derived. See, for example, [24]. Results concerning the pipe network problem treated as an optimization problem are given in Hall [14] Collins et al. 11] Dembo et al. 12] 27] 28] 29] One observation about Colebrook White facilitates the application of the convex optimization method. The integral of is as ....

A.L. Peressini, F.E. Sullivan and J.J. Uhl, The mathematics of nonlinear programming. (Springer-Verlag, U.S.A.: 1988).

....simulation to check the quality of numerical simulation results, but here strategies for dealing with modeling failures in an automated design system are also not discussed. A great deal of work has been done in the area of numerical optimization algorithms [Gill et al. 1981, Vanderplaats 1984, Peressini et al. 1988, Mor e and Wright 1993, Papalambros and Wilde 1988] though not much has been published about the particular difficulties of attempting to optimize functions defined by large real world numerical simulators. A number of research efforts have combined AI techniques with numerical optimization ....

Anthony L. Peressini, Francis E. Sullivan, and J. J. Uhl, Jr. The Mathematics of Nonlinear Programming. Springer-Verlag, New York, 1988.

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A.L. Peressini, F.E. Sullivan, K.J. Uhl, The Mathematics of Nonlinear Programming, Springer, New York, 1988.

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A. L. Peressini, F. E. Sullivan, and K. J. Uhl. The mathematics of nonlinear programming. Springer-Verlag, New York, 1988.

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A. L. Peressini, F. E. Sullivan, and J. J. Uhl. The Mathematics of Nonlinear Programming. Springer-Verlag, 1988.

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A. L. Peressini, F. E. Sullivan, and J. J. Uhl. The Mathematics of Nonlinear Programming. Springer-Verlag, 1988.

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A. L. Peressini, F. E. Sullivan, and J. J. Uhl. The Mathematics of Nonlinear Programming. Springer-Verlag, 1988.

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A. L. Peressini, F. E. Sullivan, and J. J. Uhl. The Mathematics of Nonlinear Programming. Springer-Verlag, 1988.

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A. L. Peressini, F. E. Sullivan, and J. J. Uhl. The Mathematics of Nonlinear Programming. Springer-Verlag, 1988.

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Antony L. Peressini, Francis E. Sullivan, and K. Jerry Uhl. The mathematics of nonlinear programming. Springer-Verlag, New York, 1988.

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A. L. Peressini, F. E. Sullivan, and J. J. Uhl. The Mathematics of Nonlinear Programming. Springer-Verlag, 1988.

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A.L. PERESSINI, F.E. SULLIVAN, and J.J. UHL, Jr. The Mathematics of Nonlinear Programming. Undergraduate texts in mathematics. Springer-Verlag, New York, 1988.

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A.L. Peressini, F.E. Sullivan, J.J. Uhl, Jr., The mathematics of nonlinear programming, Springer-Verlag, New York, 1988.

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