We consider the problem of maximizing an expected utility function of n assets, such as the mean-variance or power-utility function. Associated with a change in an asset's holdings from its current or target value...
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We consider the problem of maximizing an expected utility function of n assets, such as the mean-variance or power-utility function. Associated with a change in an asset's holdings from its current or target value is a transaction cost. This cost must be accounted for in practical problems. A straightforward way of doing so results in a 3n-dimensional optimization problem with 3n additional constraints. This higher dimensional problem is computationally expensive to solve. We present a method for solving the 3n-dimensional problem by solving a sequence of n-dimensional optimization problems, which accounts for the transaction costs implicitly rather than explicitly. The method is based on deriving the optimality conditions for the higher-dimensional problem solely in terms of lower-dimensional quantities. The new method is compared to the barrier method implemented in Cplex in a series of numerical experiments. With small but positive transaction costs, the barrier method and the new method solve problems in roughly the same amount of execution time. As the size of the transaction cost increases, the new method outperforms the barrier method by a larger and larger factor.
A deterministic global optimization algorithm is proposed for generalized geometric programming (GGP). By utilizing some transformations, the initial non-convex problem is reduced to a reverse convex programming (RCP)...
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A deterministic global optimization algorithm is proposed for generalized geometric programming (GGP). By utilizing some transformations, the initial non-convex problem is reduced to a reverse convex programming (RCP), where the objective function and constraint functions are convex. Then a linear relaxation of the problem (RCP) is obtained based on the linear lower bounding functions of the convex constraint functions and the linear upper bounding functions of the reverse convex constraint functions inside some hyperrectangle region. A cutting-plane method is proposed to add some effective linear constraints to the linear relaxation programming based on the famous arithmetic-geometric mean inequality, then derive a tighter linear relaxation programming. The proposed global optimization algorithm which connects the branch and bound method with the cutting-plane method successfully is convergent to the global minimum through the successive refinement of the linear relaxation of the feasible region of the objective function and the solutions of a series of linear relaxation problems. And finally the numerical experiment is given to illustrate the feasibility and the robust stability of the present algorithm. (c) 2005 Elsevier Inc. All rights reserved.
This paper exposes an interior-point method used to solve convex programming problems raised by limit analysis in mechanics. First we explain the main features of this method, describing in particular its typical iter...
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This paper exposes an interior-point method used to solve convex programming problems raised by limit analysis in mechanics. First we explain the main features of this method, describing in particular its typical iteration. Secondly, we show and study the results of its application to a concrete limit analysis problem, for a large range of sizes, and we compare them for validation with existing results and with those of linearized versions of the problem. As one of the objectives of the work, another classical problem is analysed for a Gurson material, to which linearization or conic programming does not apply. Copyright (c) 2005 John Wiley & Sons, Ltd.
We propose a new method for selecting a common subset of explanatory variables where the aim is to model several response variables. The idea is a natural extension of the LASSO technique proposed by Tibshirani (1996)...
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We propose a new method for selecting a common subset of explanatory variables where the aim is to model several response variables. The idea is a natural extension of the LASSO technique proposed by Tibshirani (1996) and is based on the (joint) residual sum of squares while constraining the parameter estimates to lie within a suitable polyhedral region. The properties of the resulting convex programming problem are analyzed for the special case of an orthonormal design. For the general case, we develop an efficient interior point algorithm. The method is illustrated on a dataset with infrared spectrometry measurements on 14 qualitatively different but correlated responses using 770 wavelengths. The aim is to select a subset of the wavelengths suitable for use as predictors for as many of the responses as possible.
This paper considers the multi-objective linear programming problem and discusses the case in which the coefficients of the objective function are fuzzy random variables. First, the fuzzy goal is introduced into the o...
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This paper considers the multi-objective linear programming problem and discusses the case in which the coefficients of the objective function are fuzzy random variables. First, the fuzzy goal is introduced into the objective function, considering the fuzzy decision of the human decision-maker. We consider a model in which the possibility or the necessity that the objective function value achieves the fuzzy goal is maximized on the basis of fuzzy programming or possibility programming. It is noted that the possibility or necessity fluctuates stochastically, and a decision-making process based on the stochastic programming model is proposed. After modifying the problem with constraint into an equivalent deterministic problem, the convex programming problem with a parameter is introduced. Then, an algorithm is proposed in which the optimal solution is derived, combining nonlinear programming and the bisection method. (C) 2004 Wiley Periodicals, Inc.
In this paper we consider the collection of convex programming problems with inequality and equality constraints, in which every problem of the collection is obtained by linear perturbations of the cost function and r...
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In this paper we consider the collection of convex programming problems with inequality and equality constraints, in which every problem of the collection is obtained by linear perturbations of the cost function and right-hand side perturbation of the constraints, while the "core'' cost function and the left-hand side constraint functions are kept fixed. The main result shows that the set of the problems which are not well-posed is sigma-porous in a certain strong sense. Our results concern both the infinite and finite dimensional case. In the last case the conclusions are significantly sharper.
Two new approaches to the optimal synthesis of difference patterns are proposed that can deal in an effective fashion with arbitrary sidelobe bounds. The first approach, which amounts to solving a convex programming p...
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Two new approaches to the optimal synthesis of difference patterns are proposed that can deal in an effective fashion with arbitrary sidelobe bounds. The first approach, which amounts to solving a convex programming problem, can be applied to completely arbitrary (fixed geometry) arrays and it is capable of taking into account additional constraints. The second approach, which amounts to solving a simpler linear programming problem, can be applied to uniformly spaced linear or planar arrays, and allows results about the uniqueness of the solution to be inferred. Numerical examples show the flexibility and effectiveness of the proposed procedures.
We propose a new conditional epsilon-subgradient method intended for solving general convex programs, Convergence properties of the method are investigated. It is proved that for a linear program with a compact set of...
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We propose a new conditional epsilon-subgradient method intended for solving general convex programs, Convergence properties of the method are investigated. It is proved that for a linear program with a compact set of solutions, the method generates a sequence of feasible approximations whose objective function values converge to the optimal value at a rate that is at least linear.
We study the issue of updating the analytic center after multiple cutting planes have been added through the analytic center of the current polytope. This is an important issue that arises at every stage of cutting-pl...
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We study the issue of updating the analytic center after multiple cutting planes have been added through the analytic center of the current polytope. This is an important issue that arises at every stage of cutting-plane algorithms. If q <= n cuts are to be added, we show that we can use a selective orthonormalization procedure to modify the cuts before adding them;it is then easy to identify a direction for an affine step into the interior of the new polytope and the next analytic center is then found in O( q log q) Newton steps. Further, we show that multiple cut variants with selective orthonormalization of standard interior-point cutting-plane algorithms have the same complexity as the original algorithms.
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