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21.
Jose Manuel Corcuera Joao Guerra David Nualart Wim Schoutens 《Applied Mathematics and Optimization》2006,53(3):279-309
In this paper we consider the optimal investment problem in a market where the stock price process is modeled by a geometric
Levy process (taking into account jumps).
Except for the geometric Brownian model and the geometric Poissonian model, the
resulting models are incomplete and there are many equivalent martingale measures.
However, the model can be completed by the so-called power-jump assets. By doing this we allow investment in these new assets
and we can try to maximize the expected utility of these portfolios. As particular cases we obtain the optimal portfolios
based in stocks
and bonds, showing that the new assets are superfluous for certain martingale measures
that depend on the utility function we use. 相似文献
22.
In this paper we propose a general integration scheme for a Multi-Criteria Decision Making model of the Multi-Attribute Utility
Theory in Constraint Programming. We introduce the Choquet integral as a general aggregation function for multi-criteria optimization
problems and define the Choquet global constraint that propagates this function during the Branch-and-Bound search. Finally the benefits of the propagation
of the Choquet constraint are evaluated on the examination timetabling problem. 相似文献
23.
We present a new verified optimization method to find regions for Hénon systems where the conditions of chaotic behaviour
hold. The present paper provides a methodology to verify chaos for certain mappings and regions. We discuss first how to check
the set theoretical conditions of a respective theorem in a reliable way by computer programs. Then we introduce optimization
problems that provide a model to locate chaotic regions. We prove the correctness of the underlying checking algorithms and
the optimization model. We have verified an earlier published chaotic region, and we also give new chaotic places located
by the new technique. 相似文献
24.
Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically
by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually
employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be
“close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence
many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report
results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process
can be improved to better reflect the actual properties sought.
In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend
themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms
of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling
approach may possibly lead to algorithms with improved efficiency.
AMS subject classification (2000) 65L05, 65M32, 65N21, 65N22, 65D18 相似文献
25.
In this paper, nonconvex multiobjective optimization problems are studied. New characterizations of a properly efficient solution in the sense of Geoffrion's are established in terms of the stability of one scalar optimization problem and the existence of an exact penalty function of a scalar constrained program, respectively. One of the characterizations is applied to derive necessary conditions for a properly efficient control-parameter pair of a nonconvex multiobjective discrete optimal control problem with linear constraints. 相似文献
26.
Silvia Vogel 《Annals of Operations Research》2006,142(1):269-282
The paper considers upper semicontinuous behavior in distribution of sequences of random closed sets. Semiconvergence in distribution
will be described via convergence in distribution of random variables with values in a suitable topological space. Convergence
statements for suitable functions of random sets are proved and the results are employed to derive stability statements for
random optimization problems where the objective function and the constraint set are approximated simultaneously.
The author is grateful to two anonymous referees for helpful suggestions. 相似文献
27.
A nonclassical problem is considered for the transport equation with coefficients depending on the energy of radiation. The task is to find the discontinuity surfaces for the coefficients of the equation from measurements of the radiation flux leaving the medium. For this tomography problem, an optimization problem is stated and numerically analyzed. The latter consists in determining the radiation energy that ensures the best reconstruction of the unknown medium. A simplified optimization problem is solved analytically. 相似文献
28.
Victor A. Kovtunenko 《Mathematical Methods in the Applied Sciences》2003,26(5):359-374
The 3D‐elasticity model of a solid with a plane crack under the stress‐free boundary conditions at the crack is considered. We investigate variations of a solution and of energy functionals with respect to perturbations of the crack front in the plane. The corresponding expansions at least up to the second‐order terms are obtained. The strong derivatives of the solution are constructed as an iterative solution of the same elasticity problem with specified right‐hand sides. Using the expansion of the potential and surface energy, we consider an approximate quadratic form for local shape optimization of the crack front defined by the Griffith criterion. To specify its properties, a procedure of discrete optimization is proposed, which reduces to a matrix variational inequality. At least for a small load we prove its solvability and find a quasi‐static model of the crack growth depending on the loading parameter. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
29.
In this paper, we formulate the l
p
-norm optimization problem as a conic optimization problem, derive its duality properties (weak duality, zero duality gap, and primal attainment) using standard conic duality and show how it can be solved in polynomial time applying the framework of interior-point algorithms based on self-concordant barriers. 相似文献
30.
We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth
domains in ℝ2. A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated
on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used
to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in
the case where the principal part of the differential operator is the Laplacian.
Online publication 23 January 2004. 相似文献