Results 21 to 30 of about 2,308 (150)

Lipschitz functions with maximal Clarke subdifferentials are generic [PDF]

Proceedings of the American Mathematical Society, 2000
We show that on a separable Banach space most Lipschitz functions have maximal Clarke subdifferential mappings. In particular, the generic nonexpansive function has the dual unit ball as its Clarke subdifferential at every point. Diverse corollaries are given.
Borwein, Jonathan M., Wang, Xianfu
openaire   +1 more source

Parameter Optimization of Droop Controllers for Microgrids in Islanded Mode by the SQP Method with Gradient Sampling

Complexity, Volume 2021, Issue 1, 2021., 2021
For enhancing the stability of the microgrid operation, this paper proposes an optimization model considering the small‐signal stability constraint. Due to the nonsmooth property of the spectral abscissa function, the droop controller parameters’ optimization is a nonsmooth optimization problem.
Peijie Li, Ziyi Yang, Shuchen Huang, Jun Zhang, Chun Wei   +4 more
wiley   +1 more source

A Nonpenalty Neurodynamic Model for Complex‐Variable Optimization

Discrete Dynamics in Nature and Society, Volume 2021, Issue 1, 2021., 2021
In this paper, a complex‐variable neural network model is obtained for solving complex‐variable optimization problems described by differential inclusion. Based on the nonpenalty idea, the constructed algorithm does not need to design penalty parameters, that is, it is easier to be designed in practical applications.
Bao Liu, Xuehui Mei, Haijun Jiang, Lijun Wu, Sundarapandian Vaidyanathan   +4 more
wiley   +1 more source

Lipschitz functions with maximal Clarke subdifferentials are staunch [PDF]

Bulletin of the Australian Mathematical Society, 2005
In a recent paper we have shown that most non-expansive Lipschitz functions (in the sense of Baire's category) have a maximal Clarke subdifferential. In the present paper, we show that in a separable Banach space the set of non-expansive Lipschitz functions with a maximal Clarke subdifferential is not only generic, but also staunch in the space of non ...
Borwein, Jonathan M., Wang, Xianfu
openaire   +1 more source

Jacobian Consistency of a Smoothing Function for the Weighted Second‐Order Cone Complementarity Problem

Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021
In this paper, a weighted second‐order cone (SOC) complementarity function and its smoothing function are presented. Then, we derive the computable formula for the Jacobian of the smoothing function and show its Jacobian consistency. Also, we estimate the distance between the subgradient of the weighted SOC complementarity function and the gradient of ...
Wenli Liu, Xiaoni Chi, Qili Yang, Ranran Cui, Guoqiang Wang   +4 more
wiley   +1 more source

Sufficient optimality conditions and duality for nonsmooth multiobjective optimization problems via higher order strong convexity [PDF]

Yugoslav Journal of Operations Research, 2017
In this paper, we define some new generalizations of strongly convex functions of order m for locally Lipschitz functions using Clarke subdifferential.
Upadhyay Balendu B., Priyobarta Ningthoujam, Rohen Yumnam S.   +2 more
doaj   +1 more source

Stationary Condition for Borwein Proper Efficient Solutions of Nonsmooth Multiobjective Problems with Vanishing Constraints

Mathematics, 2022
This paper discusses optimality conditions for Borwein proper efficient solutions of nonsmooth multiobjective optimization problems with vanishing constraints. A new notion in terms of contingent cone and upper directional derivative is introduced, and a
Hui Huang, Haole Zhu
doaj   +1 more source

Multivalued nonmonotone dynamic boundary condition

Boundary Value Problems, 2021
In this paper, we introduce a new class of hemivariational inequalities, called dynamic boundary hemivariational inequalities, reflecting the fact that the governing operator is also active on the boundary.
Khadija Aayadi, Khalid Akhlil, Sultana Ben Aadi, Mourad El Ouali   +3 more
doaj   +1 more source

On generalized derivatives for C1,1 vector optimization problems

Journal of Applied Mathematics, 2003
We introduce generalized definitions of Peano and Riemann directional derivatives in order to obtain second-order optimality conditions for vector optimization problems involving C1,1 data.
Davide La Torre
doaj   +1 more source

Necessary and sufficient condition on global optimality without convexity and second order differentiability [PDF]

, 2012
The main goal of this paper is to give a necessary and sufficient condition of global optimality for unconstrained optimization problems, when the objective function is not necessarily convex. We use Gâteaux differentiability of the objective function
A. Brøndsted, A.D. Ioffe, A.D. Ioffe, F.H. Clarke, I. Ekeland, J.B. Hiriart-Urruty, J.F. Bonnans, P.G. Georgiev, Pál Burai, R.T. Rockafellar   +9 more
core   +1 more source