Results 21 to 30 of about 1,586 (206)

Constructing a subgradient from directional derivatives for functions of two variables [PDF]

Journal of Nonsmooth Analysis and Optimization, 2020
For any scalar-valued bivariate function that is locally Lipschitz continuous and directionally differentiable, it is shown that a subgradient may always be constructed from the function's directional derivatives in the four compass directions, arranged ...
Kamil A. Khan, Yingwei Yuan
doaj   +1 more source

Regularity Conditions for Non-Differentiable Infinite Programming Problems using Michel-Penot Subdifferential [PDF]

Control and Optimization in Applied Mathematics, 2016
In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are locally Lipschitz.
Nader Kanzi
doaj  

Relaxed submonotone mappings

Abstract and Applied Analysis, 2003
The notions of relaxed submonotone and relaxed monotone mappings in Banach spaces are introduced and many of their properties are investigated. For example, the Clarke subdifferential of a locally Lipschitz function in a separable Banach space is relaxed
Tzanko Donchev, Pando Georgiev
doaj   +1 more source

Optimality Conditions for Properly Efficient Solutions of Nonsmooth Multiobjective GSIP [PDF]

Control and Optimization in Applied Mathematics
This paper aims to establish first-order necessary optimality conditions for non-smooth multi-objective generalized semi-infinite programming problems. These problems involve inequality constraints whose index set depends on the decision vector, and all ...
Ali Asghar Hojatifard, Nader Kanzi, Shahriar Farahmand Rad   +2 more
doaj   +1 more source

A State‐Adaptive Koopman Control Framework for Real‐Time Deformable Tool Manipulation in Robotic Environmental Swabbing

Advanced Robotics Research, EarlyView.
This work presents a state‐adaptive Koopman linear quadratic regulator framework for real‐time manipulation of a deformable swab tool in robotic environmental sampling. By combining Koopman linearization, tactile sensing, and centroid‐based force regulation, the system maintains stable contact forces and high coverage across flat and inclined surfaces.
Siavash Mahmoudi, Amirreza Davar, Dongyi Wang   +2 more
wiley   +1 more source

Superposition operator problems of Hölder-Lipschitz spaces

Demonstratio Mathematica
Let ff be a function defined on the real line, and Tf{T}_{f} be the corresponding superposition operator which maps hh to Tf(h){T}_{f}\left(h), i.e., Tf(h)=f∘h{T}_{f}\left(h)=f\circ h. In this article, the sufficient and necessary conditions such that Tf{
Niu Yeli, Wang Heping
doaj   +1 more source

Optimal Boundary Control of Non-Isothermal Viscous Fluid Flow

Fluids, 2019
We study an optimal control problem for the mathematical model that describes steady non-isothermal creeping flows of an incompressible fluid through a locally Lipschitz bounded domain.
Evgenii S. Baranovskii, Anastasia A. Domnich, Mikhail A. Artemov   +2 more
doaj   +1 more source

Characterization of Strict Convexity for Locally Lipschitz Functions

Rocky Mountain Journal of Mathematics, 2009
It is well known that a smooth function \(f: X\to\mathbb{R}\) is convex iff \(f''(x;h, h)\geq 0\) for all \(x\in X\) and all \(h\in X\). The function \(f\) is strictly convex iff \(f''(x;h,h)> 0\) for ``almost'' all \(x\in X\) and all \(h\in X\). Here \[ f''(x;u,v)= \lim_{t\to 0} \frac{\langle\nabla f(x+ tu)-\nabla f(x),v\rangle}{t}, \] where \(\nabla ...
openaire   +3 more sources

Continuity characterisations of differentiability of locally Lipschitz functions [PDF]

Bulletin of the Australian Mathematical Society, 1990
Recently David Preiss contributed a remarkable theorem about the differentiability of locally Lipschitz functions on Banach spaces which have an equivalent norm differentiable away from the origin. Using his result in conjunction with Frank Clarke's non-smooth analysis for locally Lipschitz functions, continuity characterisations of differentiability ...
Giles, J. R., Sciffer, Scott
openaire   +2 more sources

Programmable Flocks: Hierarchical Swarm Control via Dynamic Parameter Injection

Advanced Intelligent Systems, EarlyView.
We present a method for the control of robot swarms which allows the shaping and the translation of patterns of simple robots (“smart particles”), using two types of devices. These two types represent a hierarchy: a larger group of simple, oblivious robots (which we call the workers) that is governed by simple local attraction forces and a smaller ...
Vivek Shankar Varadharajan, Giovanni Beltrame   +1 more
wiley   +1 more source