2014/08/23 by Hesam Ahmadi, Ahmadi, Hesam, Uday V. Shanbhag +1 · 1 citation
Computer Science · Engineering · Medicine · #Aortic aneurysm repair treatments #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1408.5532
openalex publication_date 2014/08/23 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We consider a misspecified optimization problem that requires minimizing a\nfunction f(x;q*) over a closed and convex set X where q* is an unknown vector\nof parameters that may be learnt by a parallel learning process. In this\ncontext, We examine the development of coupled schemes that generate iterates\nxk,qk as k goes to infinity, then xk converges x*, a minimizer of\nf(x;q*) over X and qk converges to q*. In the first part of the paper, we\nconsider the solution of problems where f is either smooth or nonsmooth under\nvarious convexity assumptions on function f. In addition, rate statements are\nalso provided to quantify the degradation in rate resulted from learning\nprocess. In the second part of the paper, we consider the solution of\nmisspecified monotone variational inequality problems to contend with more\ngeneral equilibrium problems as well as the possibility of misspecification in\nthe constraints. We first present a constant steplength misspecified\nextragradient scheme and prove its asymptotic convergence. This scheme is\nreliant on problem parameters (such as Lipschitz constants)and leads us to\npresent a misspecified variant of iterative Tikhonov regularization. Numerics\nsupport the asymptotic and rate statements.\n