On implementing a primal-dual interior-point method for conic quadratic optimization

By Erling D. Andersen, Kees Roos, Tamás Terlaky. Mathematical programming, 2003

714 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c4d0ef861a09f74250fa6bceaa72aa1ecdd4d971

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In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Autonomous Trajectory Planning for Rendezvous and Proximity Operations by Conic Optimization (2012, methodology): “Themethodology described in this paper has been implemented in YALMIP, a MATLAB-based rapid-algorithm development environment, and MOSEK, a primal-dual interior-point algorithm [20] for SOCP problems, for the following numerical results.”
Stochastic Inequality Constrained Closed-loop Model Predictive Control: With Application To Chemical Process Operation (2004, background): “Both commercial software (Andersen et al., 2000) as well as non-commercial packages (Sturm, 1999) are available to solve second-order cone programs, not to mention all semi-definite programming codes.”
Solving Nonconvex Optimal Control Problems by Convex Optimization (2014, methodology): “The optimization algorithm for SOCP used together with YALMIP in this paper is a state-of-the-art primal-dual interior-point algorithm implemented in the software MOSEK [6].”
A Conic Quadratic Format for the Load Flow Equations of Meshed Networks (2007, background): “An introduction to conic programming is given in [4].”
Applications of Second Order Cone Programming (2012, background): “Andersen et al. (2003) define a general cone optimisation problem to be: (P) Minimise cTx, (3) subject to Ax = b , x ∈ K, where K is a proper cone and all other quantities have conforming dimension and A is of full row rank.”
Formulation and solution of some plasticity problems as conic programs (2007, methodology): “…any problems, in theory or in practice and, using various other concepts developed within the optimization community over the last few decades, practical algorithms applicable to realistic large-scale problems have been developed, e.g., (Sturm, 1999; Andersen et al., 2003; Tutuncu et al., 2003).”
Limit analysis of plates using the EFG method and second‐order cone programming (2009, methodology): “One of the most efficient algorithms to overcome this difficulty is the primal-dual interior-point method presented in [19,20] and implemented in commercial codes such as the Mosek software package.”
Upper bound limit analysis using simplex strain elements and second‐order cone programming (2007, methodology): “The optimal point must satisfy the following conditions [36, 37]: xi ∈ Ci ∀i ∈ {1, .”
Remarks on some properties of conic yield restrictions in limit analysis (2010, background): “Another interesting self-dual example is the rotated quadratic cone K(n) r ={x∈ |2x1x2 ‖x3:n‖(2), x1, x2 0} (3) Although this can readily be transformed into a standard quadratic cone of the form in Equation (2), it can also be treated directly in its original form [14].”
A cell‐based smoothed finite element method for kinematic limit analysis (2010, methodology): “One of the most robust and efficient algorithms to overcome this difficulty is the primal-dual interior-point method presented in [39, 40] and implemented in commercial codes such as the Mosek software package.”