Newton method of Polyak and Nesterov (2006) and of regularized Newton method of Mishchenko (2021) and Doikov and Nesterov (2021), b) we prove a local quadratic rate, which matches the best-known local rate of second-order methods, and c) our stepsize formula is simple, explicit, and does not require solving any subproblem.

Having a mixed-integer linear program (MIP) or a nonlinear program (NLP) in the second stage further aggravates the intractability, even when specialized algorithms that exploit problem structure are employed.

Theorem A.1 (Deterministic scaling limit of stochastic processes) . The reader interested in the proof is referred to the supplementary materials of [21, 31]. Although the theorem wasn't originally proven in the A.1 corresponds to 1 /δt, where δt is defined in Theorem 2.1. Before proving this proposition, we begin with a small lemma: Lemma B.2. We are now in a position to show Theorem B.1: 16 Proof.

Linear programs are often specified by hand, using prior knowledge of relevant costs and constraints.

Motivated by sequential budgeted allocation problems, we investigate online matching problems where connections between vertices are not i.i.d., but they have fixed

Solving quadratic programs (QPs) efficiently is critical to applications in finance, robotic control and operations research.

This will be proved as follows. Hence, the upper bound of condition (b) is satisfied. Now we introduce the Fano's inequality. We will use the version provided by [24] in our proofs. We firstly consider entrywise KL-divergence.

There have been many fruitful results on subspace estimation principal component analysis. Researchers have been considering random matrix with Gaussian and sub-Gaussian noise.

In this section we state some elementary results that we will use for our main proofs. The next Lemma is part of the proof of [44, Lemma 4.2], which we state here as a separate result to save some space from the longer proofs that follow later. This is part of the proof of [44, Lemma 4.2]. In this section we specialize the definitions to the case of Gaussian matrices. Lemma 7. Let n 1 be an integer, and δ (0, 1/2) .