Results 21 to 30 of about 61 (39)

Data integration with high dimensionality. [PDF]

Biometrika, 2017
Gao X, Carroll RJ.
europepmc   +1 more source

Shape retrieval using hierarchical total Bregman soft clustering. [PDF]

IEEE Trans Pattern Anal Mach Intell, 2012
Liu M, Vemuri BC, Amari S, Nielsen F.
europepmc   +1 more source

On the directional asymptotic approach in optimization theory. [PDF]

Math Program
Benko M, Mehlitz P.
europepmc   +1 more source

Isolated Calmness of Perturbation Mappings and Superlinear Convergence of Newton-Type Methods. [PDF]

J Optim Theory Appl
Benko M, Mehlitz P.
europepmc   +1 more source

A characterization of paratingent cone andP-subderivative with applications in nonsmooth analysis [PDF]

Acta Mathematica Sinica, 1991
Characterizations of the paratingent cone to an open set at a boundary point and the \(P\)-directional derivative of a real-valued continuous function are given by using the contingent cone and the contingent directional derivative, respectively. It is shown that these results are useful to establish sufficient condition for strict differentiability of
Yuntong Wang
openaire   +2 more sources

Lipschitz functions with prescribed derivatives and subderivatives

Nonlinear Analysis: Theory, Methods & Applications, 1997
The authors present a technique for constructing locally Lipschitz functions (on a separable Banach space \(X\)) which are not built-up from either convex or distance functions. In detail, in their main theorem they provide the following result: If \(f_1,f_2,\dots, f_n\) are real-valued locally Lipschitz functions on \(X\) with minimal Clarke ...
Borwein, Jonathan M., Moors, Warren B., Wang, Xianfu   +2 more
openaire   +4 more sources

Derivatives and subderivatives of buffered probability of exceedance

Operations Research Letters, 2019
Abstract In this letter, we study the derivatives and subderivatives of buffered probability of exceedance (bPOE), in which we provide the mathematical expressions with rigorous proofs for the case when bPOE is smooth. Furthermore, we extend the study to a general non-smooth case for which a set of quasigradients are explored, under a mild assumption,
Yongpei Guan, Tong Zhang, Stan Uryasev
openaire   +3 more sources

Approximate mean value theorem for upper subderivatives

Nonlinear Analysis: Theory, Methods & Applications, 1988
THE PURPOSE of this paper is to give a mean value theorem for a lower semicontinuous function f on a Banach space, using the upper subderivatives defined by Rockafellar [l]. As will be shown by example (Section 4), it may happen that the subdifferential af(x) is empty for all x in the closed line segment [a, 61, where a and b belong to X.
Dariusz Zagrodny
openaire   +3 more sources

Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming

, 1982
For finite-dimensional optimization problems with locally Lipschitzian equality and inequality constraints and also an abstract constraint described by a closed set, a Lagrange multiplier rule is derived that is sharper is in some respects than the ones of Clarke and Hiriart-Urruty.
R. T. Rockafellar
openaire   +4 more sources