We provide a lower bound showing that the O(1/k) convergence rate of NoLips method (a.k.a. Bregman Gradient or Mirror Descent) is optimal for class problems satisfying relative smoothness assumption. This assumption appeared in recent developments around method, where acceleration remained an open issue. The main inspiration behind this stems from extension performance estimation framework Dror...

A Caputo-type fractional-order mathematical model for "metapopulation cholera transmission" was recently proposed in [Chaos Solitons Fractals 117 (2018), 37--49]. sensitivity analysis of that is done here to show the accuracy relevance parameter estimation. Then, a fractional optimal control (FOC) problem formulated and numerically solved. cost-effectiveness performed assess studied measures. M...

In this paper we explore optimal liquidation in a market populated by number of heterogeneous makers that have limited inventory-carrying and risk-bearing capacity. We derive reduced form model for the dynamics their aggregated inventory considering proper scaling limit. The resulting price impact profile is shown to depend on characteristics relative importance inventories. flexible enough rep...

We examine optimal execution models that take into account both market microstructure impact and informational costs. Informational footprint is related to order flow and is represented by the trader’s influence on the flow imbalance process, while microstructure influence is captured by instantaneous price impact. We propose a continuous-time stochastic control problem that balances between th...

In modern equity markets, participants have a choice of many exchanges at which to trade. Exchanges typically operate as electronic limit order books operating under the “price-time” priority rule. Taking into account the effect of investors’ order routing decisions across exchanges, we find that the equilibrium of this decentralized market exhibits a certain state space collapse property, wher...

When planning problems have many kinds of resources or high concurrency, each optimal state has exponentially many minor variants, some of which are “better” than others. Standard methods like A∗ cannot effectively exploit these minor relative differences, and therefore must explore many redundant, clearly suboptimal plans. We describe a new optimal search algorithm for planning that leverages ...

The method of second order relative spectra has been shown to reliably approximate the discrete spectrum for a self-adjoint operator. We extend the method to normal operators and find optimal convergence rates for eigenvalues and eigenspaces. The convergence to eigenspaces is new, while the convergence rate for eigenvalues improves on the previous estimate by an order of magnitude.

In this paper we develop an economic order quantity model to investigate the optimal replenishment policies for instantaneous deteriorating items under inflation and trade credit. Demand rate is a linear function of selling price and decreases negative exponentially with time over a finite planning horizon. Shortages are allowed and partially backlogged. Under these conditions, we model the ret...