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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Adapting the interior point method for the solution of linear programs on high performance computers [PDF]
, 1991 In this paper we describe a unified algorithmic framework for the interior point method (IPM) of solving Linear Programs (LPs) which allows us to adapt it over a range of high performance computer architectures. We set out the reasons as to why IPM makes
Levkovitz, R, Mitra, G, Anderson, J
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Experimental investigations in combining primal dual interior point method and simplex based LP solvers [PDF]
, 1993 The use of a primal dual interior point method (PD) based optimizer as a robust linear programming (LP) solver is now well established. Instead of replacing the sparse simplex algorithm (SSX), the PD is increasingly seen as complementing it. The progress
Levkovitz, R +5 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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A primal–dual interior point method for a novel type-2 second order cone optimization
Results in Control and Optimization, 2021 In this paper, we define a new, special second order cone as a type-k second order cone. We focus on the case of k=2, which can be viewed as a second order conic optimization (SOCO) problem with an additional complicating variable.
Md Sarowar Morshed +2 more
doaj +1 more source
Adapting the interior point method for the solution of LPs on serial, coarse grain parallel and massively parallel computers [PDF]
, 1990 In this paper we describe a unified scheme for implementing an interior point algorithm (IPM) over a range of computer architectures. In the inner iteration of the IPM a search direction is computed using Newton's method.
Levkovitz, R +3 more
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An Algebraic-Based Primal–Dual Interior-Point Algorithm for Rotated Quadratic Cone Optimization
Computation, 2023 In rotated quadratic cone programming problems, we minimize a linear objective function over the intersection of an affine linear manifold with the Cartesian product of rotated quadratic cones.
Karima Tamsaouete, Baha Alzalg
doaj +1 more source
Learning to steer nonlinear interior-point methods
EURO Journal on Computational Optimization, 2019 Interior-point or barrier methods handle nonlinear programs by sequentially solving barrier subprograms with a decreasing sequence of barrier parameters.
Renke Kuhlmann
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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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End-To-End Resource Analysis for Quantum Interior-Point Methods and Portfolio Optimization
PRX Quantum, 2023 We study quantum interior-point methods (QIPMs) for second-order cone programming (SOCP), guided by the example use case of portfolio optimization (PO).
Alexander M. Dalzell +10 more
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