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Sparse Approximations with Interior Point Methods [PDF]
SIAM Review, 2022 Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well conditioned problems.
Valentina De Simone +4 more
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Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections [PDF]
, 2015 This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems.
Bellavia, S. +3 more
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Structure-Exploiting Interior Point Methods [PDF]
, 2020 Interior point methods are among the most popular techniques for large scale nonlinear optimization, owing to their intrinsic ability of scaling to arbitrary large problem sizes. Their efficiency has attracted in recent years a lot of attention due to increasing demand for large scale optimization in industry and engineering.
Jurai Kardos +2 more
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On the relationship of interior‐point methods
International Journal of Mathematics and Mathematical Sciences, 1992 Summary: We show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic ``paths'' that lead to a solution of the Karush-Kuhn-Tucker ...
Ruey-Lin Sheu, Shu-Cherng Fang
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The Symbolic Interior Point Method
Proceedings of the AAAI Conference on Artificial Intelligence, 2017 Numerical optimization is arguably the most prominent computational framework in machine learning and AI. It can be seen as an assembly language for hard combinatorial problems ranging from classification and regression in learning, to computing optimal policies and equilibria in decision theory, to entropy minimization in information ...
Mladenov, Martin +2 more
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An Interior-Point Method for Semidefinite Programming [PDF]
SIAM Journal on Optimization, 1996 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christoph Helmberg +3 more
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On the stationary Cahn-Hilliard equation: Interior spike solutions [PDF]
, 1998 We study solutions of the stationary Cahn-Hilliard equation in a bounded smooth domain which have a spike in the interior. We show that a large class of interior points (the "nondegenerate peak" points) have the following property: there exist such ...
Wei, J, Winter, M
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Solving the continuous nonlinear resource allocation problem with an interior point method
, 2013 Resource allocation problems are usually solved with specialized methods exploiting their general sparsity and problem-specific algebraic structure. We show that the sparsity structure alone yields a closed-form Newton search direction for the generic ...
Rohal, James J., Wright, Stephen E.
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Journal of Computational and Applied Mathematics, 2000 The simplex method starts from a basic feasible solution and moves along the boundary of the feasible region until an optimum is reached. At each step, the algorithm brings only one new variable into the basic set, regardless of the total number of variables.
Potra, Florian A., Wright, Stephen J.
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Interior point methods : current status and future directions [PDF]
, 1996 Cover title.Includes bibliographical references (leaves 23-24).Robert Freund and Shinji ...
core +3 more sources