Primal central paths and Riemannian distances for convex sets

DOI10.1007/s10208-007-9019-4zbMath1179.52013OpenAlexW2080809355WikidataQ115385154 ScholiaQ115385154MaRDI QIDQ1029546

Arkadi Nemirovski, Yu. E. Nesterov

Publication date: 13 July 2009

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10208-007-9019-4

zbMATH Keywords

convex optimizationRiemannian geometrystructural optimizationinterior-point methodspath-following methodsself-concordant functionspolynomial-time methods

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Semidefinite programming (90C22) Convex programming (90C25) Abstract computational complexity for mathematical programming problems (90C60) Interior-point methods (90C51) Convex functions and convex programs in convex geometry (52A41) Geodesics in global differential geometry (53C22)

Related Items (6)

Geodesic Walks in Polytopes ⋮ The resolvent average on symmetric cones ⋮ The membership problem for finitely generated quadratic modules in the univariate case ⋮ A Geodesic Interior-Point Method for Linear Optimization over Symmetric Cones ⋮ On the Central Path of Semidefinite Optimization: Degree and Worst-Case Convergence Rate ⋮ Randomized interior point methods for sampling and optimization

Cites Work

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• A geometric method in nonlinear programming
• Introductory lectures on convex optimization. A basic course.
• Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems
• On the Riemannian geometry defined by self-concordant barriers and interior-point methods.
• Positivitatsbereiche Im R n
• The Geometry of Algorithms with Orthogonality Constraints
• Domains of positivity

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