scholarly journals A convex-analysis perspective on disjunctive cuts

2005 ◽  
Vol 106 (3) ◽  
pp. 567-586 ◽  
Author(s):  
G. Cornuéjols ◽  
C. Lemaréchal
Keyword(s):  
Convex Analysis ◽  
Disjunctive Cuts

scholarly journals Convergence Rates of First- and Higher-Order Dynamics for Solving Linear Ill-Posed Problems

2021 ◽  
Author(s):  
Radu Boţ ◽  
Guozhi Dong ◽  
Peter Elbau ◽  
Otmar Scherzer
Keyword(s):  
Linear Operator ◽  
Operator Equation ◽  
Convex Analysis ◽  
Convergence Rates ◽  
Linear Operator Equation ◽  
Optimal Convergence Rates ◽  
Ill Posed ◽  
Thresholding Algorithm ◽  
The Given ◽  
Theoretical Results

AbstractRecently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov’s algorithm and the fast iterative shrinkage-thresholding algorithm, respectively. In this paper, we approach the solutions of linear ill-posed problems by dynamical flows. Because the squared norm of the residual of a linear operator equation is a convex functional, the theoretical results from convex analysis for energy minimising flows are applicable. However, in the restricted situation of this paper they can often be significantly improved. Moreover, since we show that the proposed flows for minimising the norm of the residual of a linear operator equation are optimal regularisation methods and that they provide optimal convergence rates for the regularised solutions, the given rates can be considered the benchmarks for further studies in convex analysis.

scholarly journals Comprehensive survey on convex analysis in robust optimization

2021 ◽  
Vol 1722 ◽  
pp. 012075
Author(s):  
D Chaerani ◽  
E Rusyaman ◽  
K R A Muslihin
Keyword(s):  
Robust Optimization ◽  
Convex Analysis ◽  
Comprehensive Survey

Pattern classification by convex analysis

1991 ◽  
Vol 8 (12) ◽  
pp. 1874 ◽  
Author(s):  
Miles N. Wernick
Keyword(s):  
Pattern Classification ◽  
Convex Analysis

scholarly journals Hyperbolic Polynomials and Convex Analysis

2001 ◽  
Vol 53 (3) ◽  
pp. 470-488 ◽  
Author(s):  
Heinz H. Bauschke ◽  
Osman Güler ◽  
Adrian S. Lewis ◽  
Hristo S. Sendov
Keyword(s):  
Convex Function ◽  
Interior Point ◽  
Convex Analysis ◽  
Symmetric Functions ◽  
Interior Point Methods ◽  
Optimization Problems ◽  
Real Polynomial ◽  
Hyperbolic Polynomials ◽  
Real Roots ◽  
Univariate Polynomial

AbstractA homogeneous real polynomial p is hyperbolic with respect to a given vector d if the univariate polynomial t ⟼ p(x − td) has all real roots for all vectors x. Motivated by partial differential equations, Gårding proved in 1951 that the largest such root is a convex function of x, and showed various ways of constructing new hyperbolic polynomials. We present a powerful new such construction, and use it to generalize Gårding’s result to arbitrary symmetric functions of the roots. Many classical and recent inequalities follow easily. We develop various convex-analytic tools for such symmetric functions, of interest in interior-point methods for optimization problems over related cones.

scholarly journals Subdifferential Calculus Rules in Convex Analysis: A Unifying Approach Via Pointwise Supremum Functions

2008 ◽  
Vol 19 (2) ◽  
pp. 863-882 ◽  
Author(s):  
A. Hantoute ◽  
M. A. López ◽  
C. Zălinescu
Keyword(s):  
Convex Analysis ◽  
Subdifferential Calculus ◽  
Calculus Rules
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