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.
core +4 more sources
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 +5 more
core +8 more sources
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
core +6 more sources
Interior-point algorithms for a class of convex optimization problems [PDF]
Yugoslav Journal of Operations Research, 2009 In this paper we consider interior-point methods (IPM) for the nonlinear, convex optimization problem where the objective function is a weighted sum of reciprocals of variables subject to linear constraints (SOR).
Lešaja Goran, Slaughter Verlynda N.
doaj +1 more source
Volumetric Barrier Cutting Plane Algorithms for Stochastic Linear Semi-Infinite Optimization
IEEE Access, 2020 In this paper, we study the two-stage stochastic linear semi-infinite programming with recourse to handle uncertainty in data defining (deterministic) linear semi-infinite programming.
Baha Alzalg, Asma Gafour, Lewa Alzaleq
doaj +1 more source
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
core +4 more sources
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
doaj +1 more source
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
openaire +5 more sources
Convergence analysis of an Inexact Infeasible Interior Point method for Semidefinite Programming [PDF]
, 2004 In this paper we present an extension to SDP of the well known infeasible Interior Point method for linear programming of Kojima,Megiddo and Mizuno (A primal-dual infeasible-interior-point algorithm for Linear Programming, Math. Progr., 1993).
Pieraccini, Sandra +2 more
core +1 more source