No abstract

No abstract

We analyze the proximal alternating linearized minimization algorithm (PALM) for solving non-smooth convex minimization problems where the objective function is a sum of a smooth convex function and block separable non-smooth extended real-valued convex functions. We prove a global non-asymptotic sublinear rate of convergence for PALM. When the number of blocks is two, and the smooth coupling function is quadratic we present a fast version of PALM which is proven to share a global sublinear rate efficiency estimate improved by a squared root factor. Some numerical examples illustrate the potential benefits of the proposed schemes.

We consider the class of nondifferentiable convex problems which minimizes a nonsmooth convex objective over a single smooth constraint. Exploiting the smoothness of the feasible set and using duality, we introduce a simple first order algorithm proven to globally converge to an optimal solution with a O(1/ε) efficiency estimate. The performance of the algorithm is demonstrated by solving large instances of the convex sparse recovery problem.

Background: Despite advances in treatments, 30% to 50% of stage III-IV head and neck squamous cell carcinoma (HNSCC) patients relapse within 2 years after treatment. The Big Data to Decide (BD2Decide) project aimed to build a database for prognostic prediction modeling. Methods: Stage III-IV HNSCC patients with locoregionally advanced HNSCC treated with curative intent (1537) were included. Whole transcriptomics and radiomics analyses were performed using pretreatment tumor samples and computed tomography/magnetic resonance imaging scans, respectively. Results: The entire cohort was composed of 71% male (1097)and 29% female (440): oral cavity (429, 28%), oropharynx (624, 41%), larynx (314, 20%), and hypopharynx (170, 11%); median follow-up 50.5 months. Transcriptomics and imaging data were available for 1284 (83%) and 1239 (80%) cases, respectively; 1047 (68%) patients shared both. Conclusions: This annotated database represents the HNSCC largest available repository and will enable to develop/validate a decision support system integrating multiscale data to explore through classical and machine learning models their prognostic role.