{"paper":{"title":"On the rate analysis of inexact augmented Lagrangian schemes for convex optimization problems with misspecified constraints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"H. Ahmadi, N. S. Aybat, U. V. Shanbhag","submitted_at":"2015-10-02T04:47:18Z","abstract_excerpt":"We consider a misspecified optimization problem that requires minimizing of a convex function $f(x;\\theta^*)$ in x over a constraint set represented by $h(x;\\theta^*)\\leq 0$, where $\\theta^*$ is an unknown (or misspecified) vector of parameters. Suppose $\\theta^*$ can be learnt by a distinct process that generates a sequence of estimators $\\theta_k$, each of which is an increasingly accurate approximation of $\\theta^*$. We develop a first-order augmented Lagrangian scheme for computing an optimal solution $x^*$ while simultaneously learning $\\theta^*$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00490","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}