Figure 4 - uploaded by Andrew R. Conn
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Two fiber networks are compared. Backbone node is shown in black, potential revenue generating premises are shown in grey, street corners and zero revenue producing premises are shown in white. Deployed fiber is shown in bold. The top network provides service to all potential revenue generating premises while bottom network provides service only to profitable premises.
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Citations
... Recent work from the nonlinear programming community [18] [19] has emphasized the need to monitor the " geometry " of the sample points even when using them to build a local quadratic approximation to the objective—in particular, to avoid the numerical ill-conditioning that can arise if such considerations are ignored. Furthermore, a standard theme in global optimization [20] [21] [22] is the need to sample in regions where relatively little is known about the objective in an effort to devise heuristics that are more likely to produce global minimizers. ...
. Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem often are computationally intensive. Within a standard nonlinear optimization algorithm, the computational expense of evaluating the functions that define the problem would necessarily be incurred for each iteration of the optimization algorithm. Faced with such prohibitive computational costs, an attractive alternative is to make use of surrogates within an optimization context since surrogates can be chosen or constructed so that they are typically much less expensive to compute. For the purposes of this paper, we will focus on the use of algebraic approximations as surrogates for the objective. In this paper we introduce the use of so-called merit functions that explicitly recognize the desirability of improving the...
. Recently, Resende and Veiga [31] have proposed an efficient implementation of the Dual Affine (DA) interior-point algorithm for the solution of linear transportation models with integer costs and right-hand side coefficients. This procedure incorporates a Preconditioned Conjugate Gradient (PCG) method for solving the linear system that is required in each iteration of the DA algorithm. In this paper, we introduce an Incomplete QR Decomposition (IQRD) preconditioning for the PCG algorithm. Computational experience shows that the IQRD preconditioning is quite appropriate in this instance and is more efficient than the preconditioning introduced by Resende and Veiga. We also show that the Primal Dual (PD) and the Predictor Corrector (PC) interior point algorithms can also be implemented by using the same type of technique. A comparison among these three algorithms is also included and indicates that the PD an PC algorithms are more appropriate for the solution of transportation problems...
