Results 211 to 220 of about 8,616 (247)

Convex composite non-Lipschitz programming

Mathematical Programming, 2002
Necessary and sufficient optimality conditions are given for the following problem: \[ \min(g\circ F)(x),\text{ s.t. }x\in C,\;f_i(x)\leq 0,\;i=1,2, \dots, m \] where \(F:\mathbb{R}^n\to \mathbb{R}^m\) is a continuous nonsmooth map, \(g:\mathbb{R}^m \to\mathbb{R}\) is a convex function, \(C\subset R^n\) is a closed convex set, and \(f_i:\mathbb{R}^n ...
Jeyakumar, V., Luc, D. T., Tinh, P. N.
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STOCHASTIC DIFFERENTIAL UTILITY UNDER NON-LIPSCHITZ CONDITIONS

Acta Mathematica Scientia, 2000
Let \(W\) denote a standard Brownian motion. The announced aim of the paper is to study one-dimensional backward stochastic differential equations (BSDE) \[ dY_t(\omega)= -f(t,\omega, Y_t(\omega)) dt+ Z_t(\omega) dW_t(\omega),\quad t\in [0,T],\quad Y_T= \xi\in L^2(\Omega,{\mathcal F},P), \] under non-Lipschitz conditions on the driving coefficient \(f\)
Zhou, Shaofu, Wang, Xiangjun
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Approximation of BSDE with non Lipschitz coefficient

Stochastic Analysis and Applications, 2021
In this paper we study the discrete approximation of backward stochastic differential equations.
D. Borkowski, K. Jańczak-Borkowska
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Non-Lipschitz approach to quantum mechanics

Chaos, Solitons & Fractals, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Concentration of non‐Lipschitz functions and applications

Random Structures & Algorithms, 2002
AbstractStrong concentration results play a fundamental role in probabilistic combinatorics and theoretical computer science. In this paper, we present several new concentration results developed recently by the author and collaborators. To illustrate the power of these new results, we discuss applications in many different areas of mathematics, from ...
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Linearly Constrained Non-Lipschitz Optimization for Image Restoration

SIAM Journal on Imaging Sciences, 2015
Summary: Nonsmooth nonconvex optimization models have been widely used in the restoration and reconstruction of real images. In this paper, we consider a linearly constrained optimization problem with a non-Lipschitz regularization term in the objective function which includes the \(l_p\) norm ...
Bian, Wei, Chen, Xiaojun
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Variational analysis of non-Lipschitz spectral functions

Mathematical Programming, 2001
Let \(M^n\) be the space of \(n\times n\) complex matrices, and let \[ \lambda :M^n\rightarrow \mathbb{C}^n,\;\lambda (X)=(\lambda _1(X),\dots ,\lambda_n(X)) \] be the eigenvalue map, where \(\lambda_1(X),\dots ,\lambda_n(X)\) denote (repeated according to multiplicity) the eigenvalues of \(X\) ordered lexicographically: if \(k\operatorname{Re ...
Burke, James V., Overton, Michael L.
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An Augmented Lagrangian Method for Non-Lipschitz Nonconvex Programming

SIAM Journal on Numerical Analysis, 2017
In this interesting article, optimization problems of minimizing nonconvex and possibly non-Lipschitz continuous functions over some feasible set are investigated. First, it is shown that the Karush-Kuhn-Tucker conditions (KKT) are necessary optimality conditions under the relaxed constant positive linear dependence constraint qualification (RCPLD ...
Xiaojun Chen, Lei Guo, Zhaosong Lu
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Generalized fractional BSDE with non Lipschitz coefficients

Afrika Matematika, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aïdara, Sadibou, Sow, Ahmadou Bamba
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Generalized Solutions to a Non Lipschitz-Cauchy Problem

Journal of Applied Analysis, 2009
Summary: We investigate solutions to a semilinear partial differential equation with non Lipschitz nonlinearity by using recent theories of generalized functions. To give a meaning to a non Lipschitz characteristic Cauchy problem with irregular data, we replace it by a three parameter family of problems.
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