Results 1 to 10 of about 3,697 (188)

On the theory of subdifferentials

Advances in Nonlinear Analysis, 2012
The theory presented in the paper consists of two parts. The first is devoted to basic concepts and principles such as the very concept of a subdifferential, trustworthiness and its characterizations, geometric consistence, fuzzy principles and calculus ...
Ioffe Alexander D.
exaly   +3 more sources

Symplectic Bregman Divergences [PDF]

Entropy
We present a generalization of Bregman divergences in finite-dimensional symplectic vector spaces that we term symplectic Bregman divergences. Symplectic Bregman divergences are derived from a symplectic generalization of the Fenchel–Young inequality ...
Frank Nielsen
doaj   +2 more sources

A Path Algorithm for Constrained Estimation [PDF]

J Comput Graph Stat, 2011
Many least squares problems involve affine equality and inequality constraints. Although there are variety of methods for solving such problems, most statisticians find constrained estimation challenging.
Brunk H. D., Chen X., de Leeuw J., Dempster A. P., Efron B., Efron B., Friedman J., Friedman J., Goodnight J. H., Grenander U., Groeneboom P., Hanson D. L., Hildreth C., Hua Zhou, Jennrich R., Kenneth Lange, Lange K., Lawson C. L., Li C., Little R. J. A., Liu J., Magnus J. R., Mammen E., Meyer M., Nocedal J., Robertson T., Rosset S., Ruszczyński A., Savage C., Schoenfeld D. A., Shen X., Silvapulle M. J., Stein C. M., Tibshirani R., Tibshirani R. J., Wu T. T., Zou H.   +36 more
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Directed Subdifferentiable Functions and the Directed Subdifferential without Delta-Convex Structure [PDF]

Journal of Optimization Theory and Applications, 2013
We show that the directed subdifferential introduced for differences of convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from the directional derivative without using any information on the DC structure of the function.
Baier, Robert, Farkhi, Elza, Roshchina, Vera   +2 more
core   +3 more sources

A generalization of interval-valued optimization problems and optimality conditions by using scalarization and subdifferentials

Kuwait Journal of Science, 2021
In this work, interval-valued optimization problems are considered. Ordering cone is used in order to obtain a generalization of interval-valued optimization problems on real topological vector spaces.
Emrah KARAMAN
doaj   +1 more source

Quasi Efficient Solutions and Duality Results in a Multiobjective Optimization Problem with Mixed Constraints via Tangential Subdifferentials

Mathematics, 2022
We take up a nonsmooth multiobjective optimization problem with tangentially convex objective and constraint functions. In employing a suitable constraint qualification, we formulate both necessary and sufficient optimality conditions for (local) quasi ...
Mohsine Jennane, El Mostafa Kalmoun, Lahoussine Lafhim, Anouar Houmia   +3 more
doaj   +1 more source

Fréchet Analysis and Sensitivity Relations for the Optimal Time Problem

IEEE Access, 2020
In this paper, we first present formulas for computing the Fréchet subdifferentials and Fréchet singular subdifferentials of the minimal time function $\mathscr {T}$ for a differential inclusion in $\mathbb {R}^{n}$ with a general ...
Luong V. Nguyen, Nguyen T. Thu
doaj   +1 more source

Second-order subdifferential calculus with applications to tilt stability in optimization [PDF]

, 2011
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the so-called (full
Mordukhovich, B. S., Rockafellar, R. T.
core   +4 more sources

Constrained Nonsmooth Problems of the Calculus of Variations

, 2021
The paper is devoted to an analysis of optimality conditions for nonsmooth multidimensional problems of the calculus of variations with various types of constraints, such as additional constraints at the boundary and isoperimetric constraints.
Dolgopolik, M. V.
core   +1 more source

About [q]-regularity properties of collections of sets [PDF]

, 2014
We examine three primal space local Hoelder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations.
Kruger, Alexander Y., Thao, Nguyen H.
core   +3 more sources