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40
A trust region method based on interior point techniques for nonlinear programming
 Mathematical Programming
, 1996
"... Jorge Nocedal z An algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints is described. It applies sequential quadratic programming techniques to a sequence of barrier problems, and uses trust regions to ensure the robustness of the iteration and to allow the direc ..."
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Cited by 105 (18 self)
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Jorge Nocedal z An algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints is described. It applies sequential quadratic programming techniques to a sequence of barrier problems, and uses trust regions to ensure the robustness of the iteration and to allow the direct use of second order derivatives. This framework permits primal and primaldual steps, but the paper focuses on the primal version of the new algorithm. An analysis of the convergence properties of this method is presented. Key words: constrained optimization, interior point method, largescale optimization, nonlinear programming, primal method, primaldual method, SQP iteration, barrier method, trust region method.
Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation
, 2008
"... The widelyused estimator of Berry, Levinsohn and Pakes (1995) produces consistent instrumental variables estimates of consumer preferences from a discretechoice demand model with random coefficients, marketlevel demand shocks and potentially endogenous regressors (prices). The nested fixedpoint ..."
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Cited by 20 (0 self)
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The widelyused estimator of Berry, Levinsohn and Pakes (1995) produces consistent instrumental variables estimates of consumer preferences from a discretechoice demand model with random coefficients, marketlevel demand shocks and potentially endogenous regressors (prices). The nested fixedpoint algorithm typically used for estimation is computationally intensive, largely because a system of market share equations must be repeatedly numerically inverted. We provide numerical theory results that characterize the properties of typical nested fixedpoint implementations. We use these results to discuss several problems with typical computational implementations and, in particular, cases which can lead to incorrect parameter estimates. As a solution, we introduce a new computational formulation of the estimator that recasts estimation as a mathematical program with equilibrium constraints (MPEC). In many instances, MPEC is faster than the nested fixed point approach. It also avoids the numerical issues associated with nested inner loops. Several Monte Carlo experiments support our numerical concerns about NFP and the advantages of MPEC. We also discuss estimating static BLP using maximum likelihood instead of GMM. Finally, we show that MPEC is particularly attractive for forwardlooking demand models where
Mesh ShapeQuality Optimization Using the Inverse MeanRatio Metric
 Preprint ANL/MCSP11360304, Argonne National Laboratory, Argonne
, 2004
"... 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 finiteelement method, for solving a partial differential equation. Moreover, such meshes can lead to poor accuracy in the approximate ..."
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Cited by 14 (4 self)
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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 finiteelement 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 vertices of a given mesh to optimize the average element shape quality as measured by the inverse meanratio metric. To solve the resulting largescale optimization problems, we apply an efficient implementation of an inexact Newton algorithm using the conjugate gradient method with a block Jacobi preconditioner to compute the direction. We show that the block Jacobi preconditioner is positive definite by proving a general theorem concerning the convexity of fractional functions, applying this result to components of the inverse meanratio metric, and showing that each block in the preconditioner is invertible. Numerical results obtained with this specialpurpose code on several test meshes are presented and used to quantify the impact on solution time and memory requirements of using a modeling language and generalpurpose algorithm to solve these problems. 1
Portfolio Selection with Robust Estimation
 SUBMITTED TO OPERATIONS RESEARCH
, 2007
"... Meanvariance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly outofsample due to estimation error. Moreover, it is commonly accepted that estimation error in the sample mean is much larger than in the sample covariance matrix. For this reason, pra ..."
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Cited by 10 (0 self)
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Meanvariance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly outofsample due to estimation error. Moreover, it is commonly accepted that estimation error in the sample mean is much larger than in the sample covariance matrix. For this reason, practitioners and researchers have recently focused on the minimumvariance portfolio, which relies solely on estimates of the covariance matrix, and thus, usually performs better outofsample. But even the minimumvariance portfolios are quite sensitive to estimation error and have unstable weights that fluctuate substantially over time. In this paper, we propose a class of portfolios that have better stability properties than the traditional minimumvariance portfolios. The proposed portfolios are constructed using certain robust estimators and can be computed by solving a single nonlinear program, where robust estimation and portfolio optimization are performed in a single step. We show analytically that the resulting portfolio weights are less sensitive to changes in the assetreturn distribution than those of the traditional minimumvariance portfolios. Moreover, our numerical results on simulated and empirical data confirm that the proposed portfolios are more stable than the traditional minimumvariance portfolios, while preserving (or slightly improving) their relatively good outofsample performance.
Constrained Minimum Crest Factor Multisine Signals for "PlantFriendly" Identification of Highly Interactive Systems
 In: 13th IFAC Symp. on System Identification. Rotterdam
, 2003
"... Highly interactive systems are illconditioned and highly sensitive to model uncertainty, which imposes limitations to achievable closedloop performance. In this paper, the goal is to develop an identification testing framework meaningful to highly interactive systems based on the application of ..."
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Cited by 7 (5 self)
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Highly interactive systems are illconditioned and highly sensitive to model uncertainty, which imposes limitations to achievable closedloop performance. In this paper, the goal is to develop an identification testing framework meaningful to highly interactive systems based on the application of constrained minimum crest factor multisine signals.
An interiorpoint method for MPECs based on strictly feasible relaxations
 PREPRINT ANL/MCSP11500404, MATHEMATICS AND COMPUTER SCIENCE DIVISION, ARGONNE NATIONAL LABORATORY, ARGONNE, IL
, 2004
"... An interiorpoint method for solving mathematical programs with equilibrium constraints (MPECs) is proposed. At each iteration of the algorithm, a single primaldual step is computed from each subproblem of a sequence. Each subproblem is defined as a relaxation of the MPEC with a nonempty strictly ..."
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Cited by 6 (0 self)
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An interiorpoint method for solving mathematical programs with equilibrium constraints (MPECs) is proposed. At each iteration of the algorithm, a single primaldual step is computed from each subproblem of a sequence. Each subproblem is defined as a relaxation of the MPEC with a nonempty strictly feasible region. In contrast to previous approaches, the proposed relaxation scheme preserves the nonempty strict feasibility of each subproblem even in the limit. Local and superlinear convergence of the algorithm is proved even with a less restrictive strict complementarity condition than the standard one. Moreover, mechanisms for inducing global convergence in practice are proposed. Numerical results on the MacMPEC test problem set demonstrate the fastlocal convergence properties of the algorithm.
Fuzzy Trust Integration for Security Enforcement in Grid Computing
 in Proceedings of IFIP International Conf. on Network and Parallel Computing, (NPC2004
, 2004
"... Abstract. How to build the mutual trust among Grid resources sites is crucial to secure distributed Grid applications. We suggest enhancing the trust index of resource sites by upgrading their intrusion defense capabilities and checking the success rate of jobs running on the platforms. We propose a ..."
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Cited by 6 (1 self)
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Abstract. How to build the mutual trust among Grid resources sites is crucial to secure distributed Grid applications. We suggest enhancing the trust index of resource sites by upgrading their intrusion defense capabilities and checking the success rate of jobs running on the platforms. We propose a new fuzzylogic trust model for securing Grid resources. Grid security is enforced through trust update, propagation, and integration across sites. Fuzzy trust integration reduces platform vulnerability and guides the defense deployment across Grid sites. We developed a SeGO scheduler for trusted Grid resource allocation. The SeGO scheduler optimizes the aggregate computing power with security assurance under fixed budget constraints. The effectiveness of the scheme was verified by simulation experiments. Our results show up to 90% enhancement in site security. Compared with no trust integration, our scheme leads to 114 % improvement in Grid performance/cost ratio. The job drop rate reduces by 75%. The utilization of Grid resources increased to 92.6 % as more jobs are submitted. These results demonstrate significant performance gains through optimized resource allocation and aggressive security reinforcement. 1.
A Barrier Algorithm for Large Nonlinear Optimization Problems
, 2003
"... that I have read this dissertation and that, in my ..."
OptimizationBased Design of PlantFriendly Input Signals Using Geometric Discrepancy Criteria
 14 th IFAC Symposium on System Identification (SYSID 2006
, 2006
"... Abstract: The design of constrained, “plantfriendly ” multisine input signals that optimize a geometric discrepancy criterion arising from Weyl’s Theorem is examined in this paper. Such signals are meaningful for datacentric estimation methods, where uniform coverage of the output statespace is c ..."
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Cited by 3 (1 self)
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Abstract: The design of constrained, “plantfriendly ” multisine input signals that optimize a geometric discrepancy criterion arising from Weyl’s Theorem is examined in this paper. Such signals are meaningful for datacentric estimation methods, where uniform coverage of the output statespace is critical. The usefulness of this problem formulation is demonstrated by applying it to a linear example and to the nonlinear, highly interactive distillation column model developed by Weischedel and McAvoy (1980). The optimization problem includes a search for both the Fourier coefficients and phases in the multisine signal, resulting in an uniformly distributed output signal displaying a desirable balance between high and low gain directions. The solution involves very little user intervention (which enhances its practical usefulness) and has significant benefits compared to multisine signals that minimize crest factor.