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作者：Sim, Chee-Khian; Zhao, Gongyun
作者单位：National University of Singapore; National University of Singapore
摘要：An interior point method defines a search direction at each interior point of the feasible region. The search directions at all interior points together form a direction field, which gives rise to a system of ordinary differential equations (ODEs). Given an initial point in the interior of the feasible region, the unique solution of the ODE system is a curve passing through the point, with tangents parallel to the search directions along the curve. We call such curves off-central paths. We stu...
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作者：Karakostas, George; Viglas, Anastasios
作者单位：University of Sydney; McMaster University
摘要：We consider the problem of characterizing user equilibria and optimal solutions for selfish routing in a given network. We extend the known models by considering malicious behavior. While selfish users follow a strategy that minimizes their individual cost, a malicious user will use his flow through the network in an effort to cause the maximum possible damage to the overall cost. We define a generalized model, present characterizations of flows at equilibrium and prove bounds for the ratio of...
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作者：Jeyakumar, V.; Rubinov, A. M.; Wu, Z. Y.
作者单位：University of New South Wales Sydney; Federation University Australia; Chongqing Normal University
摘要：In this paper, we first examine how global optimality of non-convex constrained optimization problems is related to Lagrange multiplier conditions. We then establish Lagrange multiplier conditions for global optimality of general quadratic minimization problems with quadratic constraints. We also obtain necessary global optimality conditions, which are different from the Lagrange multiplier conditions for special classes of quadratic optimization problems. These classes include weighted least ...
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作者：Munson, Todd
作者单位：United States Department of Energy (DOE); Argonne National Laboratory
摘要：Meshes containing elements with bad quality can result in poorly conditioned systems of equations that must be solved when using a discretization method, such as the finite-element method, for solving a partial differential equation. Moreover, such meshes can lead to poor accuracy in the approximate solution computed. In this paper, we present a nonlinear fractional program that relocates the vertex coordinates of a given mesh to optimize the average element shape quality as measured by the in...
