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Title of Journal: Comput Optim Appl

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Abbravation: Computational Optimization and Applications

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Springer US

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1573-2894

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On the resolution of certain discrete univariate m

Authors: Ramsharan Rangarajan
Publish Date: 2017/03/06
Volume: 68, Issue: 1, Pages: 163-192
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Abstract

We analyze a class of discrete univariate and strictly quasiconcave max–min problems A distinctive feature of max–mintype optimization problems is the nonsmoothness of the objective being maximized Here we exploit strict quasiconcavity of the given set of functions to prove existence and uniqueness of the optimizer and to provide computable bounds for it The analysis inspires an efficient algorithm for computing the optimizer without having to resort to any regularization or heuristics We prove correctness of the proposed algorithm and briefly discuss the effect of tolerances and approximate computation Our study finds direct application in the context of certain mesh deformation methods wherein the optimal perturbation for a vertex is computed as the solution of a max–min problem of the type we consider here We include examples demonstrating improvement of simplicial meshes while adopting the proposed algorithm for resolution of the optimization problems involved and use these numerical experiments to examine the performance of the algorithm

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  1. A benchmark library and a comparison of heuristic methods for the linear ordering problem
  2. Compression and denoising using l 0 -norm
  3. AAR-based decomposition algorithm for non-linear convex optimisation
  4. Classification of companies using maximal margin ellipsoidal surfaces
  5. Multi-step nonlinear conjugate gradient methods for unconstrained minimization
  6. Optimization-based design of plant-friendly multisine signals using geometric discrepancy criteria
  7. Minimization of the Tikhonov functional in Banach spaces smooth and convex of power type by steepest descent in the dual
  8. Numerical experiments with an inexact Jacobian trust-region algorithm
  9. An interior-point approach for primal block-angular problems
  10. Computing the metric dimension of graphs by genetic algorithms
  11. Some non-interior path-following methods based on a scaled central path for linear complementarity problems
  12. A coordinate gradient descent method for ℓ 1 -regularized convex minimization
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