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991.
We compute constrained equilibria satisfying an optimality condition. Important examples include convex programming, saddle
problems, noncooperative games, and variational inequalities. Under a monotonicity hypothesis we show that equilibrium solutions
can be found via iterative convex minimization. In the main algorithm each stage of computation requires two proximal steps,
possibly using Bregman functions. One step serves to predict the next point; the other helps to correct the new prediction.
To enhance practical applicability we tolerate numerical errors.
Research supported partly by the Norwegian Research Council, project: Quantec 111039/401. 相似文献
992.
M. A. Morón C. Romero F. R. Ruiz del Portal 《Journal of Optimization Theory and Applications》1996,91(3):643-649
The purpose of this paper is to seek utility functions satisfying a weak condition which guarantees that the utility optimum always belongs to the compromise set. This set is a special subset of the attainable or feasible set, which is generated through the application of the well-known operational research approach called compromise programming. It is shown that there are large families of utility functions satisfying this condition, thus reinforcing the value of compromise programming as a good surrogate of the traditional utility optimum.Thanks are due to the reviewers for their helpful suggestions. The English editing by Ms. Christine Méndez is appreciated. The authors have been supported by the Comisión Interministerial de Ciencia y Tecnología (CICYT), Madrid, Spain. 相似文献
993.
P. A. V. Ferreira M. E. S. Machado 《Journal of Optimization Theory and Applications》1996,89(3):659-680
Projection and relaxation techniques are employed to decompose a multiobjective problem into a two-level structure. The basic manipulation consists in projecting the decision variables onto the space of the implicit tradeoffs, allowing the definition of a relaxed multiobjective master problem directly in the objective space. An additional subproblem tests the feasibility of the solution encountered by the relaxed problem. Some properties of the relaxed problem (linearity, small number of variables, etc.) render its solution efficient by a number of methods. Representatives of two different classes of multiobjective methods [the Geoffrion, Dyer, Feinberg (GDF) method and the fuzzy method of Baptistella and Ollero] are implemented and applied within this context to a water resources allocation problem. The results attest the computational viability of the overall procedure and its usefulness for the solution of multiobjective problems.This work was partially sponsored by grants from CNPq and FAPESP, Brazil. The authors are indebted to the anonymous reviewers for their valuable comments. 相似文献
994.
995.
Pravin M. Vaidya 《Mathematical Programming》1996,73(3):291-341
Let
be a convex set for which there is an oracle with the following property. Given any pointz∈ℝ
n
the oracle returns a “Yes” ifz∈S; whereas ifz∉S then the oracle returns a “No” together with a hyperplane that separatesz fromS. The feasibility problem is the problem of finding a point inS; the convex optimization problem is the problem of minimizing a convex function overS. We present a new algorithm for the feasibility problem. The notion of a volumetric center of a polytope and a related ellipsoid
of maximum volume inscribable in the polytope are central to the algorithm. Our algorithm has a significantly better global
convergence rate and time complexity than the ellipsoid algorithm. The algorithm for the feasibility problem easily adapts
to the convex optimization problem. 相似文献
996.
M. Sun 《Applied Mathematics and Optimization》1996,34(3):267-277
We focus on numerically solving a typical type of Hamilton-Jacobi-Bellman (HJB) equations arising from a class of optimal controls with a standard multidimensional diffusion model. Solving such an equation results in the value function and an optimal feedback control law. The Bellman's curse of dimensionality seems to be the main obstacle to applicability of most numerical algorithms for solving HJB. We decompose HJB into a number of lower-dimensional problems, and discuss how the usual alternating direction method can be extended for solving HJB. We present some convergence results, as well as preliminary experimental outcomes.This research was funded in part by an RGC grant from the University of Alabama. 相似文献
997.
998.
999.
The purpose of this paper is to present a method to compute optimal controls for a class of one-dimensional heat-diffusion processes. The approach used is in the spirit of the Ritz method and approximates the given problem with simpler tasks which are solved by means of algorithms based on the principles of semi-infinite programming. General convergence properties of the procedures are shown. Some illustrative numerical examples are also given.This research was supported by NSF Grant No. GK-31833 and by The Swedish Institute of Applied Mathematics, Stockholm, Sweden. 相似文献
1000.
Muhammad Fawad Khan Muhammad Sulaiman Carlos Andrs Tavera Romero Ali Alkhathlan 《Entropy (Basel, Switzerland)》2021,23(11)
A unipolar electrohydrodynamic (UP-EHD) pump flow is studied with known electric potential at the emitter and zero electric potential at the collector. The model is designed for electric potential, charge density, and electric field. The dimensionless parameters, namely the electrical source number , the electrical Reynolds number , and electrical slip number , are considered with wide ranges of variation to analyze the UP-EHD pump flow. To interpret the pump flow of the UP-EHD model, a hybrid metaheuristic solver is designed, consisting of the recently developed technique sine–cosine algorithm (SCA) and sequential quadratic programming (SQP) under the influence of an artificial neural network. The method is abbreviated as ANN-SCA-SQP. The superiority of the technique is shown by comparing the solution with reference solutions. For a large data set, the technique is executed for one hundred independent experiments. The performance is evaluated through performance operators and convergence plots. 相似文献