2,209 research outputs found
Sample-path solutions for simulation optimization problems and stochastic variational inequalities
inequality;simulation;optimization
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
Solving Variational Inequalities with Monotone Operators on Domains Given by Linear Minimization Oracles
The standard algorithms for solving large-scale convex-concave saddle point
problems, or, more generally, variational inequalities with monotone operators,
are proximal type algorithms which at every iteration need to compute a
prox-mapping, that is, to minimize over problem's domain the sum of a
linear form and the specific convex distance-generating function underlying the
algorithms in question. Relative computational simplicity of prox-mappings,
which is the standard requirement when implementing proximal algorithms,
clearly implies the possibility to equip with a relatively computationally
cheap Linear Minimization Oracle (LMO) able to minimize over linear forms.
There are, however, important situations where a cheap LMO indeed is available,
but where no proximal setup with easy-to-compute prox-mappings is known. This
fact motivates our goal in this paper, which is to develop techniques for
solving variational inequalities with monotone operators on domains given by
Linear Minimization Oracles. The techniques we develope can be viewed as a
substantial extension of the proposed in [5] method of nonsmooth convex
minimization over an LMO-represented domain
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