The work of three leading figures in the early history of econometrics is used to motivate some recent developments in the theory and application of quantile regression. We stress not only the robustness advantages of...
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The work of three leading figures in the early history of econometrics is used to motivate some recent developments in the theory and application of quantile regression. We stress not only the robustness advantages of this form of semiparametric statistical method, but also the opportunity to recover a more complete description of the statistical relationship between variables. A recent proposal for a more X-robust form of quantile regression based on maximal depth ideas is described along with an interesting historical antecedent. Finally, the notorious computational burden of median regression, and quantile regression more generally, is addressed. It is argued that recent developments in interiorpointmethods for linearprogramming together with some new preprocessing ideas make it possible to compute quantile regressions as quickly as least-squares regressions throughout the entire range of problem sizes encountered in econometrics. (C) 2000 Elsevier Science S.A. All rights reserved.
This paper establishes theorems about the simultaneous variation of right-hand sides and cost coefficients in a linear program from a strictly complementary solution. Some results are extensions of those that have bee...
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This paper establishes theorems about the simultaneous variation of right-hand sides and cost coefficients in a linear program from a strictly complementary solution. Some results are extensions of those that have been proven for varying the right-hand side of the primal or the dual, but not both;other results are new. In addition, changes in the optimal partition and what that means in economic terms are related to the basis-driven approach, notably to the theory of compatibility. In addition to new theorems about this relation, the transition graph is extended to provide another visualization of the underlying economics.
Economic dispatching of electrical energy is an approach to the operation of power systems concerned with the interrelations between power system variables and the mathematical procedures for arriving at the best oper...
Economic dispatching of electrical energy is an approach to the operation of power systems concerned with the interrelations between power system variables and the mathematical procedures for arriving at the best operational state, given the system physical properties, technical constraints, and stated objective. Different approaches have been published describing the dispatching problem in mathematical terms and its corresponding solution method. The most popular algorithms applied to the dispatching problems are in essence active set methods. In practice, the active set methods exhibit a significant increase in computational effort on large dispatching problems as is confirmed by the need to introduce decomposition methods into the dispatching solution. A quest for fast, accurate and robust methods continues. Path-following interior-pointmethods have recently emerged as polynomial time algorithms with excellent performance on large linearprogramming problems. This research aims to bridge the gap between interior-pointmethods and economic dispatching problems. In this thesis, different models of economic dispatching are formulated by refining the modelling accuracy of the transmission network. The related problems are formulated as linear, non-linear convex and non-linear non-convex programs. A general path-following interior-point method is presented in symmetric form, which is shown to be superior to the asymmetric form traditionally used in interior-pointmethods for economic dispatching. A modification technique for the treatment of indefiniteness in the reduced Hessian is put forward to enhance convergence when solving non-convex dispatching problems. A novel implementation of the homogeneous interiorpoint method is proposed for the solution of convex economic dispatching problems in order to overcome the disadvantages of standard interior-pointmethods, i. e. mainly the choice of an initial point and the reliable detection of infeasibility. Strategies, wh
This paper deals with an algorithm incorporating the interior-point method into the Dantzig-Wolfe decomposition technique for solving large-scale linearprogramming problems, The algorithm decomposes a linear program ...
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This paper deals with an algorithm incorporating the interior-point method into the Dantzig-Wolfe decomposition technique for solving large-scale linearprogramming problems, The algorithm decomposes a linear program into a main problem and a subproblem. The subproblem is solved approximately. Hence, inexact Newton directions are used in solving the main problem. We show that the algorithm is globally linearly convergent and has polynomial-time complexity.
In this paper, we study the minimization of the max function of q smooth convex functions on a domain specified by infinitely many linear constraints. The difficulty of such problems arises from the kinks of the max f...
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In this paper, we study the minimization of the max function of q smooth convex functions on a domain specified by infinitely many linear constraints. The difficulty of such problems arises from the kinks of the max function and it is often suggested that, by imposing certain regularization functions, nondifferentiability will be overcome. We find that the entropic regularization introduced by Li and Fang is closely related to recently developed path-following interior-pointmethods. Based on their results, we create an interior trajectory in the feasible domain and propose a path-following algorithm with a convergence proof. Our intention here is to show a nice combination of minmax problems, semi-infinite programming, and interior-pointmethods, Hopefully, this will lead to new applications.
A wide variety of nonlinear convex optimization problems can be cast as problems involving linear matrix inequalities (LMIs), and hence efficiently solved using recently developed interior-pointmethods. In this paper...
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A wide variety of nonlinear convex optimization problems can be cast as problems involving linear matrix inequalities (LMIs), and hence efficiently solved using recently developed interior-pointmethods. In this paper, we will consider two classes of optimization problems with LMI constraints: (1) The semidefinite programming problem, i.e., the problem of minimizing a linear function subject to a linear matrix inequality. Semidefinite programming is an important numerical tool for analysis and synthesis in systems and control theory. It has also been recognized in combinatorial optimization as a valuable technique for obtaining bounds on the solution of NP-hard problems. (2) The problem of maximizing the determinant of a positive definite matrix subject to linear matrix inequalities. This problem has applications in computational geometry, experiment design, information and communication theory, and other fields. We review some of these applications, including some interesting applications that are less well known and arise in statistics, optimal experiment design and VLSI. (C) 1999 Elsevier Science B.V, and IMACS. All rights reserved.
We present an algorithm for variational inequalities VI(F, Y) that uses a primal-dual version of the Analytic Center Cutting Plane Method. The point-to-set mapping F is assumed to be monotone, or pseudomonotone. Each ...
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We present an algorithm for variational inequalities VI(F, Y) that uses a primal-dual version of the Analytic Center Cutting Plane Method. The point-to-set mapping F is assumed to be monotone, or pseudomonotone. Each computation of a new analytic center requires at most four Newton iterations, in theory, and in practice one or sometimes two. linear equalities that may be included in the definition of the set Y are taken explicitly into account. We report numerical experiments on several well-known variational inequality problems as well as on one where the functional results from the solution of large subproblems. The method is robust and competitive with algorithms which use the same information as this one.
Self-scaled conic programming is a generalization of the theories of linearprogramming, semidefinite programming and convex quadratic programming with convex quadratic constraints. The barrier method applied to these...
Self-scaled conic programming is a generalization of the theories of linearprogramming, semidefinite programming and convex quadratic programming with convex quadratic constraints. The barrier method applied to these optimization problems makes use of the symmetry properties of certain cones. We begin our investigations by giving a structure theorem which classifies the barrier functionals that reflect these symmetry properties and are rotationally invariant. In a second part we generalize the concepts of target map and weighted analytic centers to self-scaled conic programming. In the theory of linearprogramming these concepts allow for a unified analysis of various families of interior-pointmethods, and it can be hoped that our generalization will lead to a similar unification in the self-scaled framework. Our method defines an infinite new class of Newton directions which lend themselves to the predictor-corrector approach. We show that for each self-scaled conic programming problem there exists a direction from this family that is primal-dual symmetric and has certain other strong invariance properties. Finally, in a third part we show that Nesterov-Todd directions are special cases of target directions. In particular, it follows from this result that Nesterov-Todd directions are genuine Newton directions, and that the Nesterov-Todd process generates iterates that converge at a quadratic rate.
In an automated assembly system, a product is completed through a series of assembly operations according to a predefined sequence. Partially assembled components are automatically transported from one machine to anot...
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In an automated assembly system, a product is completed through a series of assembly operations according to a predefined sequence. Partially assembled components are automatically transported from one machine to another machine until the final product is organized. This paper describes a method for finding optimal assembly sequences in an assembly system. All feasible assembly sequences can be represented by an AND/OR graph which provides all feasible geometric configurations and relationships among the components of a product. The AND/OR graph is converted into a Petri net which can be formulated as a linear program with the objective of minimizing the total assembly time or cost. A dynamic programming algorithm is developed to find the optimal sequences from the Petri net since too much computational effort is required to obtain the optimal solution of the linear program by utilizing the simplex method and interiorpointmethods. The algorithm has the computational complexity of O(nm), where n and m denote the number of assembly operations and base components, respectively, and it is more efficient than the former methods. Three assembly products are provided to validate the algorithm.
In this paper we present an inexact interiorpoint method for solving monotone nonlinear complementarity problems. We show that the theory presented by Kojima, Noma and Yoshise for an exact version of this method can ...
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In this paper we present an inexact interiorpoint method for solving monotone nonlinear complementarity problems. We show that the theory presented by Kojima, Noma and Yoshise for an exact version of this method can be used to establish global convergence for the inexact form. Then we prove that local superlinear convergence can be achieved under some stronger hypotheses. The complexity of the algorithm is also studied under the assumption that the problem satisfies a scaled Lipschitz condition. It is proved that the feasible version of the algorithm is polynomial, while the infeasible one is globally convergent at a linear rate.
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