Journal ArticleDOI
Penalty and Smoothing Methods for Convex Semi-Infinite Programming
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This paper introduces a unified framework concerning Remez-type algorithms and integral methods coupled with penalty and smoothing methods that subsumes well-known classical algorithms, but also provides some new methods with interesting properties.Abstract:
In this paper we consider min-max convex semi-infinite programming. To solve these problems we introduce a unified framework concerning Remez-type algorithms and integral methods coupled with penalty and smoothing methods. This framework subsumes well-known classical algorithms, but also provides some new methods with interesting properties. Convergence of the primal and dual sequences are proved under minimal assumptions.read more
Citations
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Journal ArticleDOI
An Efficient Algorithm for Min-Max Convex Semi-Infinite Programming Problems
Liping Zhang,Soon-Yi Wu +1 more
TL;DR: This article is the first one conceived to apply explicit exchange methods for solving nonlinear semi-infinite convex min-max problems by using efficient inactive constraint dropping rules.
On finite convergence of an explicit exchange method for convex semi-infinite programming problems with second-order cone constraints ∗
TL;DR: In this article, the authors considered the convex semi-infinite programming problem with second-order cone con-straints and proposed an explicit exchange method for solving SOCCSIP, and proved that the algorithm terminates in a finite number of iterations under some mild conditions.
Journal ArticleDOI
A Spline Smoothing Newton Method for Semi-Infinite Minimax Problems
TL;DR: The spline smoothing Newton method uses a smooth cubic spline instead of max function and only few components in the max function are computed; that is, it introduces an active set technique, so it is more efficient for solving large-scale minimax problems arising from the discretization of semi-infinite minimax Problems.
Journal ArticleDOI
Neural networks can detect model-free static arbitrage strategies
Ariel Neufeld,Julian Sester +1 more
TL;DR: In this article , the authors demonstrate both theoretically and numerically that neural networks can detect model-free static arbitrage opportunities whenever the market admits some, which can be applied to financial markets with a high number of traded securities and ensure almost immediate execution of corresponding trading strategies.
Journal ArticleDOI
Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation
TL;DR: In this paper , the authors consider derivatives written on multiple underlyings in a one-period financial market and provide model-free upper and lower bounds for their arbitrage-free prices.
References
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Journal ArticleDOI
Smooth minimization of non-smooth functions
TL;DR: A new approach for constructing efficient schemes for non-smooth convex optimization is proposed, based on a special smoothing technique, which can be applied to functions with explicit max-structure, and can be considered as an alternative to black-box minimization.
Book
Perturbation Analysis of Optimization Problems
TL;DR: It is shown here how the model derived recently in [Bouchut-Boyaval, M3AS (23) 2013] can be modified for flows on rugous topographies varying around an inclined plane.
Journal ArticleDOI
A class of smoothing functions for nonlinear and mixed complementarity problems
Chunhui Chen,Olvi L. Mangasarian +1 more
TL;DR: A class of parametric smooth functions that approximate the fundamental plus function, (x)+=max{0, x}, by twice integrating a probability density function leads to classes of smooth parametric nonlinear equation approximations of nonlinear and mixed complementarity problems (NCPs and MCPs).