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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...
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...