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1.
We study two-period nonlinear optimization problems whose parameters are uncertain. We assume that uncertain parameters are revealed in stages and model them using the adjustable robust optimization approach. For problems with polytopic uncertainty, we show that quasiconvexity of the optimal value function of certain subproblems is sufficient for the reducibility of the resulting robust optimization problem to a single-level deterministic problem. We relate this sufficient condition to the cone-quasiconvexity of the feasible set mapping for adjustable variables and present several examples and applications satisfying these conditions. This work was partially supported by the National Science Foundation, Grants CCR-9875559 and DMS-0139911, and by Grant-in-Aid for Scientific Research from the Ministry of Education, Sports, Science and Culture of Japan, Grant 16710110.  相似文献   

2.
In this paper several parameter dependent scalarization approaches for solving nonlinear multi-objective optimization problems are discussed. It is shown that they can be considered as special cases of a scalarization problem by Pascoletti and Serafini (or a modification of this problem). Based on these connections theoretical results as well as a new algorithm for adaptively controlling the choice of the parameters for generating almost equidistant approximations of the efficient set, lately developed for the Pascoletti-Serafini scalarization, can be applied to these problems. For instance for such well-known scalarizations as the ε-constraint or the normal boundary intersection problem algorithms for adaptively generating high quality approximations are derived.  相似文献   

3.
Many financial optimization problems involve future values of security prices, interest rates and exchange rates which are not known in advance, but can only be forecast or estimated. Several methodologies have therefore, been proposed to handle the uncertainty in financial optimization problems. One such methodology is Robust Statistics, which addresses the problem of making estimates of the uncertain parameters that are insensitive to small variations. A different way to achieve robustness is provided by Robust Optimization which, given optimization problems with uncertain parameters, looks for solutions that will achieve good objective function values for the realization of these parameters in given uncertainty sets. Robust Optimization thus offers a vehicle to incorporate an estimation of uncertain parameters into the decision making process. This is true, for example, in portfolio asset allocation. Starting with the robust counterparts of the classical mean-variance and minimum-variance portfolio optimization problems, in this paper we review several mathematical models, and related algorithmic approaches, that have recently been proposed to address uncertainty in portfolio asset allocation, focusing on Robust Optimization methodology. We also give an overview of some of the computational results that have been obtained with the described approaches. In addition we analyse the relationship between the concepts of robustness and convex risk measures.  相似文献   

4.
In this short note we give two counterexamples to the Triality Theorem concerning the optimization problem presented in Ruan et al., Comput. Optim. Appl. (2008). In order to understand the problem first we introduce the framework of this paper and quote the theorem we have in view. Then, while trying to verify this theorem we encounter several difficulties and note their nature. We end by revealing our counterexamples.  相似文献   

5.
A coupled map lattice (CML) provides a mathematical model for both spatially extended physical and biological systems, and for a new type of parallel computing system. We analyse a general process to realize a multilayer structured CML by coupling m CMLs together with arbitrary coupling structure. As an application we use this coupling process in the study of a CML with multilayer planar architecture and non-symmetric hierarchical coupling between the layers. These CMLs model neural architectures and use chaotic maps as the basic elements in the lattice. We measure the complexity of the state of each layer and an increase in spatio-temporal coherence as one ascends a hierarchical feedforward layered network.  相似文献   

6.
In this paper, we consider an extend-valued nonsmooth multiobjective optimization problem of finding weak Pareto optimal solutions. We propose a class of vector-valued generalized viscosity approximation method for solving the problem. Under some conditions, we prove that any sequence generated by this method converges to a weak Pareto optimal solution of the multiobjective optimization problem.  相似文献   

7.
One of the challenging optimization problems is determining the minimizer of a nonlinear programming problem that has binary variables. A vexing difficulty is the rate the work to solve such problems increases as the number of discrete variables increases. Any such problem with bounded discrete variables, especially binary variables, may be transformed to that of finding a global optimum of a problem in continuous variables. However, the transformed problems usually have astronomically large numbers of local minimizers, making them harder to solve than typical global optimization problems. Despite this apparent disadvantage, we show that the approach is not futile if we use smoothing techniques. The method we advocate first convexifies the problem and then solves a sequence of subproblems, whose solutions form a trajectory that leads to the solution. To illustrate how well the algorithm performs we show the computational results of applying it to problems taken from the literature and new test problems with known optimal solutions.  相似文献   

8.
A two dimensional model of the orientation distribution of fibres in a paper machine headbox is studied. The goal is to control the fibre orientation distribution at the outlet of contraction by changing its shape. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Then, the problem is expressed as an optimal control problem governed by variational forms. By using an embedding method, the class of admissible shapes is replaced by a class of positive Radon measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution of this linear programming problem. In this paper, we have shown that the embedding method (embedding the admissible set into a subset of measures), successfully can be applied to shape variation design to a one dimensional headbox. The usefulness of this idea is that the method is not iterative and it does not need any initial guess of the solution.   相似文献   

9.
In many planning problems under uncertainty the uncertainties are decision-dependent and resolve gradually depending on the decisions made. In this paper, we address a generic non-convex MINLP model for such planning problems where the uncertain parameters are assumed to follow discrete distributions and the decisions are made on a discrete time horizon. In order to account for the decision-dependent uncertainties and gradual uncertainty resolution, we propose a multistage stochastic programming model in which the non-anticipativity constraints in the model are not prespecified but change as a function of the decisions made. Furthermore, planning problems consist of several scenario subproblems where each subproblem is modeled as a nonconvex mixed-integer nonlinear program. We propose a solution strategy that combines global optimization and outer-approximation in order to optimize the planning decisions. We apply this generic problem structure and the proposed solution algorithm to several planning problems to illustrate the efficiency of the proposed method with respect to the method that uses only global optimization.  相似文献   

10.
We study a shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by a generalized stationary Navier–Stokes system with nontrivial mixed boundary conditions. In this paper we prove the existence of solutions both to the generalized Navier–Stokes system and to the shape optimization problem.  相似文献   

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