Symmetric indefinite systems for interior point methods
Mathematical Programming: Series A and B
On the formulation and theory of the Newton interior-point method for nonlinear programming
Journal of Optimization Theory and Applications
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Interior Methods for Nonlinear Optimization
SIAM Review
An Interior Point Algorithm for Large-Scale Nonlinear Programming
SIAM Journal on Optimization
Solving a Class of Linearly Constrained Indefinite QuadraticProblems by D.C. Algorithms
Journal of Global Optimization
Line Search Filter Methods for Nonlinear Programming: Motivation and Global Convergence
SIAM Journal on Optimization
Mathematical Programming: Series A and B
An interior algorithm for nonlinear optimization that combines line search and trust region steps
Mathematical Programming: Series A and B
Application of lower bound direct method to engineering structures
Journal of Global Optimization
Limit analysis decomposition and finite element mixed method
Journal of Computational and Applied Mathematics
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A numerical method for the computation of shakedown loads of structures subjected to varying thermal and mechanical loading is proposed for the case of multidimensional loading spaces. The shakedown loading factors are determined based on the lower bound direct method using the von Mises yield criterion. The resulting nonlinear convex optimization problem is solved by use of the interior-point method. Although the underlying theory allows for the consideration of arbitrary numbers of loadings in principle, until now applications have been restricted to special cases, where either one or two loads vary independently. In this article, former formulations of the optimization problem are generalized for the case of arbitrary numbers of loadings. The method is implemented into an interior-point algorithm specially designed for this method. For illustration, numerical results are presented for a three-dimensional loading space applied to a square plate with a central circular hole.