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The virtual customer
, 2002
"... Communication and information technologies are adding new capabilities for rapid and inexpensive customer input to all stages of the product development (PD) process. In this article we review six webbased methods of customer input as examples of the improved Internet capabilities of communication, ..."
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Cited by 223 (27 self)
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Communication and information technologies are adding new capabilities for rapid and inexpensive customer input to all stages of the product development (PD) process. In this article we review six webbased methods of customer input as examples of the improved Internet capabilities of communication, conceptualization, and computation. For each method we give examples of userinterfaces, initial applications, and validity tests. We critique the applicability of the methods for use in the various stages of PD and discuss how they complement existing methods. For example, during the fuzzy front end of PD the information pump enables customers to interact with each other in a webbased game that provides incentives for truthtelling and thinking hard, thus providing new ways for customers to verbalize the product features that are important to them. Fast polyhedral adaptive conjoint estimation enables PD teams to screen larger numbers of product features inexpensively to identify and measure the importance of the most promising features for further development. Meanwhile, interactive webbased conjoint analysis interfaces are moving this proven set of methods to the web while exploiting new capabilities to present products, features, product use, and marketing elements in streaming multimedia representations. User design exploits the interactivity of the web to enable users to design their own virtual products thus enabling the PD team to understand complex feature interactions and enabling customers to learn their own preferences for new products. These methods can be valuable for identifying opportunities, improving the design and engineering of products, and testing ideas and concepts much earlier in the process when less time and money is at risk. As products move toward pretesting and testing, virtual concept testing on the web enables PD teams to test concepts without actually building
PrimalDual TargetFollowing Algorithms for Linear Programming
 ANNALS OF OPERATIONS RESEARCH
, 1993
"... In this paper we propose a method for linear programming with the property that, starting from an initial noncentral point, it generates iterates that simultaneously get closer to optimality and closer to centrality. The iterates follow paths that in the limit are tangential to the central path. Al ..."
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Cited by 25 (1 self)
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In this paper we propose a method for linear programming with the property that, starting from an initial noncentral point, it generates iterates that simultaneously get closer to optimality and closer to centrality. The iterates follow paths that in the limit are tangential to the central path. Along with the convergence analysis we provide a general framework which enables us to analyze various primaldual algorithms in the literature in a short and uniform way.
Conjoint Analysis, Related Modeling, and Application
 IN MARKET RESEARCH AND MODELING: PROGRESS AND PROSPECTS: A TRIBUTE
, 2002
"... Conjoint analysis has as its roots the need to solve important academic and industry problems. Elsewhere in this volume, Carroll, Arabie, and Chaturvedi (2002) detail Paul Green’s interest and contributions to the theory and practice of multidimensional scaling (MDS) and clustering to address market ..."
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Cited by 13 (1 self)
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Conjoint analysis has as its roots the need to solve important academic and industry problems. Elsewhere in this volume, Carroll, Arabie, and Chaturvedi (2002) detail Paul Green’s interest and contributions to the theory and practice of multidimensional scaling (MDS) and clustering to address marketing problems. See also Green and Carmone (1970) and Green and Rao (1972). The strengths of MDS include the ability to represent consumer multidimensional perceptions and consumer preferences relative to an existing set of products. MDS decomposes more holistic judgments to uncover these perceptions and preferences. Paul, with extensive experience in product development from his days at Dupont, sought to augment the power to MDS. He sought a means to decompose consumer preferences into the partial contribution (partworth) of product features. In this manner, researchers could not only explain the preferences of existing products, but could simulate preferences for entirely new products that were defined by feature combinations. Such a method could also be used to decompose perceptions if a perceptual variable, say “ease of use ” was used as the dependent measure rather than “preference. ” This would solve the problem of reverse mapping in MDS – the challenge of translating a point from perceptual space into a corresponding point (or set of
PROJECTIVE RENORMALIZATION FOR IMPROVING THE BEHAVIOR OF A HOMOGENEOUS CONIC LINEAR System
, 2007
"... In this paper we study the homogeneous conic system F: Ax =0, x ∈ C \{0}. We choose a point ¯s ∈ intC ∗ that serves as a normalizer and consider computational properties of the normalized system F¯s: Ax = 0, ¯s T x =1, x ∈ C. We show that the computational complexity of solving F via an interiorpo ..."
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Cited by 4 (0 self)
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In this paper we study the homogeneous conic system F: Ax =0, x ∈ C \{0}. We choose a point ¯s ∈ intC ∗ that serves as a normalizer and consider computational properties of the normalized system F¯s: Ax = 0, ¯s T x =1, x ∈ C. We show that the computational complexity of solving F via an interiorpoint method depends only on the complexity value ϑ of the barrier for C and on the symmetry of the origin in the image set H¯s: = {Ax: ¯s T x =1, x ∈ C}, where the symmetry of 0 in H¯s is sym(0,H¯s):=max{α: y ∈ H¯s ⇒−αy ∈ H¯s}. We show that a solution of F can be computed in O ( √ ϑ ln(ϑ/sym(0,H¯s)) interiorpoint iterations. In order to improve the theoretical and practical computation of a solution of F, we next present a general theory for projective renormalization of the feasible region F¯s and the image set H¯s and prove the existence of a normalizer ¯s such that sym(0,H¯s) ≥ 1/m provided that F has an interior solution. We develop a methodology for constructing a normalizer ¯s such that sym(0,H¯s) ≥ 1/m with high probability, based on sampling on a geometric random walk with associated probabilistic complexity analysis. While such a normalizer is not itself computable in stronglypolynomialtime, the normalizer will yield a conic system that is solvable in O ( √ ϑ ln(mϑ)) iterations, which is stronglypolynomialtime. Finally, we implement this methodology on randomly generated homogeneous linear programming feasibility problems, constructed to be poorly behaved. Our computational results indicate that the projective renormalization methodology holds the promise to markedly reduce the overall computation time for conic feasibility problems; for instance we observe a 46 % decrease in average IPM iterations for 100 randomly generated poorlybehaved problem instances of dimension 1000 × 5000.
Sensitivity Analysis And The Analytic Central Path
, 1998
"... The analytic central path for linear programming has been studied because of its desirable convergence properties. This dissertation presents a detailed study of the analytic central path under perturbation of both the righthand side and cost vectors for a linear program. The analysis is divided int ..."
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Cited by 2 (1 self)
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The analytic central path for linear programming has been studied because of its desirable convergence properties. This dissertation presents a detailed study of the analytic central path under perturbation of both the righthand side and cost vectors for a linear program. The analysis is divided into three parts: extensions of results required by the convergence analysis when the data is unperturbed to include that case of data perturbation, marginal analysis of the analytic center solution with respect to linear changes in the righthand side, and parametric analysis of the analytic central path under simultaneous changes in both the righthand side and cost vectors. To extend the established convergence results when the data is fixed, it is rst shown that the union of the elements comprising a portion of the perturbed analytic central paths is bounded. This guarantees the existence of subsequences that converge, but these subsequences are not guaranteed to have the same limit without further restrictions on the data movement. Sufficient conditions are provided to insure that the limit is the analytic center of the iii limiting polytope. Furthermore, as long at the data converges and the parameter of the path is approaching zero, certain components of the the analytic central path are forced to zero. Since the introduction of the analytic center to the mathematical programming community, the analytic central path has been known to be analytic in both the righthand side and cost vectors. However, since the objective function is a continuous, piecewise linear function of the righthand side, the analytic center solution is not differentiable. We show that this solution is continuous and is infinitely, continuously, onesided differentiable. Furthermore, the analytic center sol...
PROJECTIVE PRECONDITIONERS FOR IMPROVING THE BEHAVIOR OF A HOMOGENEOUS CONIC LINEAR System
"... In this paper we present a general theory for transforming a normalized homogeneous conic system F: Ax = 0, ¯s T x = 1, x ∈ C to an equivalent system via projective transformation induced by the choice of a point ˆv in the set H ◦ ¯s = {v: ¯s − AT v ∈ C ∗}. Such a projective transformation serves to ..."
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In this paper we present a general theory for transforming a normalized homogeneous conic system F: Ax = 0, ¯s T x = 1, x ∈ C to an equivalent system via projective transformation induced by the choice of a point ˆv in the set H ◦ ¯s = {v: ¯s − AT v ∈ C ∗}. Such a projective transformation serves to precondition the conic system into a system that has both geometric and computational properties with certain guarantees. We characterize both the geometric behavior and the computational behavior of the transformed system as a function of the symmetry of ˆv in H ◦ ¯s as well as the complexity parameter ϑ of the barrier for C. Under the assumption that F has an interior solution, H ◦ ¯s must contain a point v whose symmetry is at least 1/m; if we can find a point whose symmetry is Ω(1/m) then we can projectively transform the conic system to one whose geometric properties and computational complexity will be stronglypolynomialtime in m and ϑ. We present a method for generating such a point ˆv based on sampling and on a geometric random walk on H ◦ ¯s with associated complexity and probabilistic analysis. Finally, we implement this methodology on randomly generated homogeneous linear programming feasibility problems, constructed to be poorly behaved. Our computational results indicate that the projective preconditioning methodology holds the promise to markedly reduce the overall computation time for conic feasibility problems; for instance we observe a 46 % decrease in average IPM iterations for 100 randomly generated poorlybehaved problem instances of dimension 1000 × 5000.
FULL LENGTH PAPER Projective
"... renormalization for improving the behavior of a homogeneous conic linear system ..."
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renormalization for improving the behavior of a homogeneous conic linear system
InteriorPoint Algorithms for a Generalization of Linear Programming and Weighted Centering
, 2011
"... We consider an extension of ordinary linear programming (LP) that adds weighted logarithmic barrier terms for some variables. The resulting problem generalizes both LP and the problem of finding the weighted analytic center of a polytope. We show that the problem has a dual of the same form and give ..."
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We consider an extension of ordinary linear programming (LP) that adds weighted logarithmic barrier terms for some variables. The resulting problem generalizes both LP and the problem of finding the weighted analytic center of a polytope. We show that the problem has a dual of the same form and give complexity results for several different interiorpoint algorithms. We obtain an improved complexity result for certain cases by utilyzing a combination of the volumetric and logarithmic barriers. As an application we consider the complexity of solving the EisenbergGale formulation of a Fisher equilibrium problem with linear utility functions.