2018/06/18 by Martin Neuenhofen, Neuenhofen, Martin
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Advanced Optimization Algorithms Research #Complexity and Algorithms in Graphs #FOS: Mathematics #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1806.06936
openalex publication_date 2018/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a particular optimization problem that minimizes the sum of a\nnon-convex quadratic function and logarithmic barrier-functions in a\n\ℓ_\∞-trust-region (i.e. cube). Our paper covers three topics.\n We explain the relevance of the considered problem. We lay out how solutions\nof this problem can be used as efficient step-directions in solution methods\nfor nonlinear programming.\n We present a theoretical algorithm for solving the problem. We show that this\nalgorithm has weak polynomial time-complexity.\n A practical method is under development. In the outlook we discuss how the\ngiven method can be accelerated for better practical performance. We also lay\nout where the difficulties live when trying to formulate an accelerated\nprimal-dual variant.\n