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991.
Z. Y. Wu 《Journal of Global Optimization》2007,39(3):427-440
In this paper, we present sufficient global optimality conditions for weakly convex minimization problems using abstract convex
analysis theory. By introducing (L,X)-subdifferentials of weakly convex functions using a class of quadratic functions, we first obtain some sufficient conditions
for global optimization problems with weakly convex objective functions and weakly convex inequality and equality constraints.
Some sufficient optimality conditions for problems with additional box constraints and bivalent constraints are then derived.
相似文献
992.
The k-eccentricity evaluated at a point x of a graph G is the sum of the (weighted) distances from x to the k vertices farthest from it. The k-centrum is the set of vertices for which the k-eccentricity is a minimum. The concept of k-centrum includes, as a particular case, that of center and that of centroid (or median) of a graph. The absolute k-centrum is the set of points (not necessarily vertices) for which the k-eccentricity is a minimum. In this paper it will be proven that, for a weighted tree, both deterministic and probabilistic, the k-eccentricity is a convex function and that the absolute k-centrum is a connected set and is contained in an elementary path. Hints will be given for the construction of an algorithm to find the k-centrum and the absolute k-centrum. 相似文献
993.
Donald M. Topkis 《Mathematical Programming》1992,54(1-3):335-351
This paper establishes bounds on the length of certain strictly monotone paths, relative to a given linear objective function, on a polymatroid or on the base of a polymatroid. Specialized bounds are given for a strict polymatroid and for a matroid polyhedron. Bounds on the diameter are included. 相似文献
994.
G. Y. Chen 《Journal of Optimization Theory and Applications》1995,84(1):93-101
This paper deals with generalizations of the Arrow-Barankin-Blackwell theorem in locally convex spaces, partially ordered by cones whose duals have nonempty quasi-interiors.This research has been partially supported by the World Laboratory, Lausanne, Switzerland, by the Department of Mathematics, University of Pisa, Pisa, Italy, and by the National Natural Sciences Foundation of China. Useful discussions with Professor F. Ferro are gratefully acknowledged. 相似文献
995.
A STRONG OPTIMIZATION THEOREM IN LOCALLY CONVEX SPACES 总被引:1,自引:0,他引:1
This paper presents a geometric characterization of convex sets in locally convex spaces on which a strong optimization theorem of the Stegall-type holds, and gives Collier's theorem of w Asplund spaces a localized setting. 相似文献
996.
This paper presents a parametrization of all finite-dimensional, linear time-invariant controllers which asymptotically stabilize a given finite-dimensional, linear time-invariant system. Both continuous-time and discrete-time systems are considered. A potential advantage over existing parametrization schemes in the frequency domain is that the controller order can be fixed. Consequently, necessary and sufficient conditions for stabilizability via static output feedback controller are obtained and stated by the existence of a quadratic Lyapunov functionV(x):=x
T
Px such thatP satisfies a linear matrix inequality (LMI), whileP
–1 satisfies another LMI. If the controller order is not fixed a priori, then the resulting computational problem can be made convex, and a controller of order less than or equal to the plant order may always be constructed. 相似文献
997.
998.
H 《Mathematical Methods of Operations Research》1991,35(5):401-424
We give a method for solving the inclusion 0F(x), whereF is a set-valued map from a Hilbert space into a Banach space, whose graph is a closed convex set. The given algorithms are convergent if the problem is consistent and terminate after a finite number of iterations if otherwise. A convergence rate of geometrical progression is also obtained if a regularity condition of the Robinson's type is assumed.The authors are grateful to the referees for valuable comments and suggestions. Special thanks are given to Prof. S.M. Robinson for advices. 相似文献
999.
Remarks on convex cones 总被引:2,自引:0,他引:2
A. Sterna-Karwat 《Journal of Optimization Theory and Applications》1988,59(2):335-340
We point out in this note that the class of cones in a locally convex topological vector space satisfying property () or piecewise relatively weakly compact cones is exactly the class of cones admitting weakly compact bases or the class of cones whose closures admit weakly compact bases.This work was supported by a Monash University Postdoctoral Fellowship. 相似文献
1000.
Evolutionary stability, the central solution concept in evolutionary game theory, is closely related to local asymptotic stability in a certain nonlinear dynamical system operating on the state space, the so-called "replicator dynamics". However, a purely dynamical characterization of evolutionary stability is not available in an elementary manner. This characterization can be achieved by investigating so-called "derived games" which consist of mixed strategies corresponding to successful states in the original game. Using well-known facts, several characterization results are obtained within this context. These also may shed light on the extremality properties of evolutionary stability. 相似文献