130 research outputs found
A weakly convergent fully inexact Douglas-Rachford method with relative error tolerance
Douglas-Rachford method is a splitting algorithm for finding a zero of the
sum of two maximal monotone operators. Each of its iterations requires the
sequential solution of two proximal subproblems. The aim of this work is to
present a fully inexact version of Douglas-Rachford method wherein both
proximal subproblems are solved approximately within a relative error
tolerance. We also present a semi-inexact variant in which the first subproblem
is solved exactly and the second one inexactly. We prove that both methods
generate sequences weakly convergent to the solution of the underlying
inclusion problem, if any
Linearly Convergent First-Order Algorithms for Semi-definite Programming
In this paper, we consider two formulations for Linear Matrix Inequalities
(LMIs) under Slater type constraint qualification assumption, namely, SDP
smooth and non-smooth formulations. We also propose two first-order linearly
convergent algorithms for solving these formulations. Moreover, we introduce a
bundle-level method which converges linearly uniformly for both smooth and
non-smooth problems and does not require any smoothness information. The
convergence properties of these algorithms are also discussed. Finally, we
consider a special case of LMIs, linear system of inequalities, and show that a
linearly convergent algorithm can be obtained under a weaker assumption
Global weak sharp minima for convex (semi-)infinite optimization problems
AbstractWe mainly consider global weak sharp minima for convex infinite and semi-infinite optimization problems (CIP). In terms of the normal cone, subdifferential and directional derivative, we provide several characterizations for (CIP) to have global weak sharp minimum property
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