This paper focuses on the impact of the stochastic evolution of the active membership population on the mismatch between assets and liabilities of a defined benefit pension scheme. Classical results in the actuarial l...
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This paper focuses on the impact of the stochastic evolution of the active membership population on the mismatch between assets and liabilities of a defined benefit pension scheme. Classical results in the actuarial literature on pension plan population theory have been extended to the stochastic case. The paper formulates the trade-off between risk and cost of contribution strategies. Then, using a constrained nonlinear programming approach, optimal contributions strategies have been derived and the trade-off solved by means of identifying an efficient frontier. Finally, a numerical application has been carried out, showing the inefficiency of certain classical normal cost methods. (c) 2005 Elsevier B.V. All rights reserved.
We discuss a special mathematical programming problem with equilibrium constraints (MPEC), that arises in material and shape optimization problems involving the contact of a rod ora plate with a rigid obstacle. This M...
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We discuss a special mathematical programming problem with equilibrium constraints (MPEC), that arises in material and shape optimization problems involving the contact of a rod ora plate with a rigid obstacle. This MPEC can be reduced to a nonlinear programming problem with independent variables and some dependent variables implicity defined by the solution of a mixed linear complementarity problem (MLCP). A projected-gradient algorithm including a complementarity method is proposed to solve this optimization problem. Several numerical examples are reported to illustrate the efficiency of this methodology in practice.
This article presents information regarding structural reliability bounds. They have applied linear programming techniques and obtained optimal bounds for a few examples in structural mechanics. However the authors ha...
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This article presents information regarding structural reliability bounds. They have applied linear programming techniques and obtained optimal bounds for a few examples in structural mechanics. However the authors have inadvertently omitted a few useful publications on probability bounds, which contain methods of obtaining near-optimal bounds without linear programming. The authors believe that with rapidly advancing speed and capacity of computers this purely computational issue may not be a hindrance in application of the LP approach to large-scale system reliability problems.
In this paper we consider a financial market model with frictions which include transaction costs, bid-ask spread and taxes. By using optimization, linear and nonlinear programming and convex programming techniques, s...
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In this paper we consider a financial market model with frictions which include transaction costs, bid-ask spread and taxes. By using optimization, linear and nonlinear programming and convex programming techniques, several necessary and sufficient conditions are derived for the weak no-arbitrage. Some results on state prices are also provided. The results of this paper can provide at least some theoretical insight to the problem.
The container loading problem has important industrial and commercial applications. An increase in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of...
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The container loading problem has important industrial and commercial applications. An increase in the number of items in a container leads to a decrease in cost. For this reason the related optimization problem is of economic importance. In this work, a procedure based on a nonlinear decision problem to solve the cylinder packing problem with identical diameters is presented. This formulation is based on the fact that the centers of the cylinders have to be inside the rectangular box defined by the base of the container (a radius far from the frontier) and far from each other at least one diameter. With this basic premise the procedure tries to find the maximum number of cylinder centers that satisfy these restrictions. The continuous nature of the problem is one of the reasons that motivated this study. A comparative study with other methods of the literature is presented and better results are achieved. (C) 2003 Elsevier B.V. All rights reserved.
Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constr...
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Equilibrium equations in the form of complementarity conditions often appear as constraints in optimization problems. Problems of this type are commonly referred to as mathematical programs with complementarity constraints (MPCCs). A popular method for solving MPCCs is the penalty interior-point algorithm (PIPA). This paper presents an example for which PIPA converges to a nonstationary point, providing a counterexample to the established theory. The reasons for this adverse behavior are discussed.
The problem of positioning p points so as to maximize the minimum distance between them has been studied in both location theory (as the continuous p-dispersion problem) and the design of computer experiments (as the ...
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The problem of positioning p points so as to maximize the minimum distance between them has been studied in both location theory (as the continuous p-dispersion problem) and the design of computer experiments (as the maximin distance design problem). This problem can be formulated as a nonlinear program, either exactly or approximately. We consider formulations of both types and demonstrate that, as p increases, it becomes dramatically more expensive to compute solutions of the exact formulation than to compute solutions of the approximate formulation.
This paper presents a new sequential method for constrained nonlinear optimization problems. The principal characteristics of these problems are very time consuming function evaluations and the absence of derivative i...
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This paper presents a new sequential method for constrained nonlinear optimization problems. The principal characteristics of these problems are very time consuming function evaluations and the absence of derivative information. Such problems are common in design optimization, where time consuming function evaluations are carried out by simulation tools (e.g., FEM, CFD). Classical optimization methods, based on derivatives, are not applicable because often derivative information is not available and is too expensive to approximate through finite differencing. The algorithm first creates an experimental design. In the design points the underlying functions are evaluated. Local linear approximations of the real model are obtained with help of weighted regression techniques. The approximating model is then optimized within a trust region to find the best feasible objective improving point. This trust region moves along the most promising direction, which is determined on the basis of the evaluated objective values and constraint violations combined in a filter criterion. If the geometry of the points that determine the local approximations becomes bad, i.e. the points are located in such a way that they result in a bad approximation of the actual model, then we evaluate a geometry improving instead of an objective improving point. In each iteration a new local linear approximation is built, and either a new point is evaluated (objective or geometry improving) or the trust region is decreased. Convergence of the algorithm is guided by the size of this trust region. The focus of the approach is on getting good solutions with a limited number of function evaluations. (C) 2003 Elsevier B.V. All rights reserved.
In this paper we discuss the application of optimization techniques for the design of several parts of the color picture tube, the key component of television sets and computer monitors. These projects have been carri...
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In this paper we discuss the application of optimization techniques for the design of several parts of the color picture tube, the key component of television sets and computer monitors. These projects have been carried out for Philips Display Components in Eindhoven. Philips developed several computer simulation models of picture tube parts. Designers use these models to simulate the physical behavior of a particular part design. Depending on the amount of detail in the model, the running time of a typical simulation ranges from one up to 10 hours. Tube designers are confronted with the problem of finding settings for a large number of design parameters that are optimal with respect to several simulated tube characteristics. This problem can be modeled as a so-called high-cost nonlinear programming problem. This paper reports on the successful application of our four-step compact model approach to solve this problem. The presented results are based on four projects in which we optimized picture tube parts. Among the realized benefits for Philips are a design improvement of 30% and a time-to-market reduction of 50-60%. (C) 2002 Elsevier Science B.V. All rights reserved.
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