计量经济分析 = Econometric analysis

‘The Production of Space’, in: Frans Jacobi, Imagine, Space Poetry, Copenhagen, 1996, unpaginated.

The Production of Space

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Convex Analysisの二,三の進展について

The Structural Transformation of the Public Sphere: An Inquiry into a Category of Bourgeois Society

On robust estimation of the location parameter

We introduce a first order method for solving very large convex cone programs. The method uses an operator splitting method, the alternating directions method of multipliers, to solve the homogeneous self-dual embedding, an equivalent feasibility problem involving finding a nonzero point in the intersection of a subspace and a cone. This approach has several favorable properties. Compared to interior-point methods, first-order methods scale to very large problems, at the cost of requiring more time to reach very high accuracy. Compared to other first-order methods for cone programs, our approach finds both primal and dual solutions when available or a certificate of infeasibility or unboundedness otherwise, is parameter-free, and the per-iteration cost of the method is the same as applying a splitting method to the primal or dual alone. We discuss efficient implementation of the method in detail, including direct and indirect methods for computing projection onto the subspace, scaling the original problem data, and stopping criteria. We describe an open-source implementation, which handles the usual (symmetric) non-negative, second-order, and semidefinite cones as well as the (non-self-dual) exponential and power cones and their duals. We report numerical results that show speedups over interior-point cone solvers for large problems, and scaling to very large general cone programs.

Operator Splitting for Conic Optimization via Homogeneous Self-Dual Embedding

A heterogeneous multi-processor (HeMP) system consists of several heterogeneous processors, each of which is specially designed to deliver the best energy-saving performance for a particular category of applications. A low-power real-time scheduling algorithm is required to schedule tasks on such a system to minimize its energy consumption and complete all tasks by their deadline. The problem of determining the optimal speed for each processor to minimize the total energy consumption is called the voltage setup problem. This paper provides a near-optimal solution for the HeMP single-level voltage setup problem. To our best knowledge, we are the first work that addresses this problem. Initially, each task is assigned to a processor in a local-optimal manner. We next propose a couple of solutions to reduce energy by migrating tasks between processors. Finally, we determine each processor's speed by its final workload and the deadline. We conducted a series of simulations to evaluate our algorithms. The results show that the local-optimal partition leads to a considerably better energy-saving schedule than a commonly-used homogeneous multi-processor scheduling algorithm. Furthermore, at all measurable configurations, our energy consumption is at most 3% more than the optimal value obtained by an exhaustive iteration of all possible task-to-processor assignments. In summary, our work is shown to provide a near-optimal solution at its polynomial-time complexity.

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A Near-optimal Solution for the Heterogeneous Multi-processor Single-level Voltage Setup Problem

We consider the numerical solution of the nonlinear eigenvalue problemA(λ)x=0, where the matrixA(λ) is dependent on the eigenvalue parameter λ nonlinearly. Some new methods (the BDS methods) are presented, together with the analysis of the condition of the methods. Numerical examples comparing the methods are given.

On the numerical solution of nonlinear eigenvalue problems

In earlier papers, the Bauer--Fike technique [F. L. Bauer and C. T. Fike, Numer. Math., 2 (1960), pp. 137--144] was applied to the eigenvalue problem $A{\bf x} = \lambda {\bf x}$ [E. K.-W. Chu, Numer. Math., 49 (1986), pp. 685--691] and the generalized eigenvalue problem $A{\bf x} = \lambda B{\bf x}$ [E. K.-W. Chu, SIAM J. Numer. Anal., 24 (1987), pp. 1114--1125]. General multiple eigenvalues were dealt with and perturbation results were obtained for individual as well as clusters of eigenvalues. In this paper, we shall generalize the technique to the eigenvalue problem for matrix polynomials. Multiple eigenvalues for monic as well as regular matrix polynomials will be considered.

Eric Chu

Papers

Operator Splitting for Conic Optimization via Homogeneous Self-Dual Embedding

A Near-optimal Solution for the Heterogeneous Multi-processor Single-level Voltage Setup Problem

On the numerical solution of nonlinear eigenvalue problems

Perturbation of Eigenvalues for Matrix Polynomials via The Bauer--Fike Theorems

Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding