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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On strongly quasiconvex functions: existence results and proximal point algorithms
强准孔函数 存在结果 近端点算法
2023/5/4
The class of strongly quasiconvex functions was introduced in the famous paper of B.T. Polyak in 1966. It is the natural extension of the class of strongly convex functions, its applications emcompass...
Dual Representation of Quasiconvex Conditional Maps
quasiconvex functions dualrep resentation quasiconvex optimiza-tion dynamic risk measures conditionalc ertainty equivalent
2010/4/27
We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued ...
Dual Representation of Quasiconvex Conditional Maps
quasiconvex functions dualrep resentation quasiconvex optimiza-tion dynamic risk measures conditionalc ertainty equivalent
2010/4/27
We provide a dual representation of quasiconvex maps between two lattices of random variables in terms of conditional expectations. This generalizes the dual representation of quasiconvex real valued ...
Rank-one-convex and Quasiconvex Envelopes for Functions Depending on Quadratic Forms
rank-one-convex quasiconvex envelope quadratic form James-Ericksen function Pipkin's formula
2009/2/5
In this paper we are interested in functions defined, on a set of matrices, by the mean of quadratic forms and we compute the rank-one-convex, quasiconvex, polyconvex and convex envelopes of these fun...
A Generalization of the Quasiconvex Optimization Problem
Quasiconvex Optimization Problem instead of functions convex minimization problem
2009/2/5
In this paper the quasiconvex minimization problem is included in a problem defined by sets (instead of functions). Lagrangian conditions for both problems are then studied and related. Lagrangian con...
We establish (i) that the quasiconvexifcation of the distance function to any closed (possibly unbounded) subset of the space of conformal matrices $E_{\partial}$ in $M^{2\times 2}$ is bounded from be...
On the composition of quasiconvex functions and the transposition
Polyconvexity quasiconvexity rank-one convexity
2009/1/20
If $G:\mathbb{R}^{n\times m}\to\bar\mathbb{R}:=\mathbb{R}\cup\{+\infty\}$ is a convex, polyconvex or rank-one convex function, then the function $g:\mathbb{R}^{m\times n}\to\bar\mathbb{R}$ defined as ...
A New Subdifferential in Quasiconvex Analysis
Greenberg-Pierskalla quasi-subdifferential Frechet subdifferential quasiconvexity
2009/1/19
We introduce a new notion of subdifferential, which we call Q-subdifferential, for functions defined on subsets of normed spaces. The Q-subdifferential is a subset of the Greenbeg-Pierskalla quasi-sub...
Elements of Quasiconvex Subdifferential Calculus
Calculus subdifferential constructed lower subdifferential
2009/1/13
A number of rules for the calculus of subdifferentials of generalized convex functions are displayed. The subdifferentials we use are among the most significant for this class of functions, in particu...
Rank-One Connections at Infinity and Quasiconvex Hulls
Rank-One Infinity Quasiconvex Hulls
2009/1/13
We define $p$-rank-one connections at infinity for an unbounded set $K$ in $M^{N\times n}$ and show that the quasiconvex hull $Q_p(K)$ may be bigger than $K$ if $K$ has a $p$-rank-one connection, wher...
Hadamard-type Inequalities for Quasiconvex Functions
Quasiconvex function Hadamard inequality
2008/7/1
Recently Hadamard-type inequalities for nonnegative, evenly quasiconvex functions which attain their minimum have been established. We show that these inequalities remain valid for the larger class co...
Sharp Bounds on Quasiconvex Moments of Generalized Order Statistics
Generalized Order Statistics Quasiconvex Moments Moriguti Inequality Steffensen Inequality
2008/6/26
Sharp lower and upper bounds for quasiconvex moments of generalized order statistics are proven by the use of rearranged Moriguti's inequality. Even in the second moment case, the method yields improv...
Connectedness of Cone-Efficient Solution Set for Cone-Quasiconvex Multiobjective Programming
Multiobjective programming cone-efficient solution cone-quasiconvex mapping generalized saddle theorem connectedness
2007/12/11
This paper deals with the connectedness of thecone-efficient solution set for vector optimization in locallyconvex Hausdorff topological vector spaces.The connectedness of thecone-efficient solution s...
A Class of Cone Bounded Quasiconvex Mappings in Topological Vector Spaces
cone convexity cone quasiconvexity
2007/12/10
Within the context of cone-ordered topological vector spaces, this paper introduces the concepts of cone bounded point and cone bounded set for vector set. With their aid, a class of new cone quasicon...