We consider a broker who has to place a large order which consumes a sizable part of average daily trading volume. The broker’s aim is thus to minimize execution costs he incurs from the adverse impact of his trades on market prices. In contrast to the previous literature (see, e.g., Obizhaeva and Wang [A. Obizhaeva and J. Wang, J. Financial Markets, 16 (2013), pp. 1–32] and Predoiu, Shaikhet, ...

The paper presents necessary and sufficient conditions for the order reduction of optimal control systems. Exploring the corresponding Hamiltonian system allows to solve the order reduction problem in terms of dynamical systems, observability and invariant differential forms. The approach is applicable to non-degenerate optimal control systems with smooth integral cost function. The cost functi...

We give two new D-optimal designs of order 110.

This paper presents an algorithm to triangulate polygons optimally using order-k Delaunay triangulations, for a number of quality measures. The algorithm uses properties of higher order Delaunay triangulations to improve the O(n) running time required for normal triangulations to O(kn log k + kn log n) expected time, where n is the number of vertices of the polygon. An extension to polygons wit...

We consider a problem of optimal order allocation faced for example by an internet trading agent who seeks to ful…l an order for speci…ed amounts of several products from a pre-arranged list of suppliers, taking into account availability and price. We present a mixed integer programming (MILP) formulation for the case that suppliers impose a …xed charge which is waived or discounted on orders a...

Proportional Integral Derivative (PID) controllers are widely used in industrial processes for their simplicity and robustness. The main application problems are the tuning of PID parameters to obtain good settling time, rise time and overshoot. The challenge is to improve the timing parameters to achieve optimal control performances. Remarkable findings are obtained through the use of Artifici...

Given a sequence of numbers ul,. ,a,,, find a binary tree with q leaves minimizing max{/l, + (II,. , II,, + u, }, where h, is the distance from the ith leaf to the root, i = I, , q. This problem is solved by means of a O(q) algorithm and a tight upper bound for the minimum is given by an explicit formula. The task is equivalent to finding a binary tree of minimum height having y subtrees of hei...

Partial-order plans (POPs) are attractive because of their least-commitment nature, which provides enhanced plan flexibility at execution time relative to sequential plans. Current research on automated plan generation focuses on producing sequential plans, despite the appeal of POPs. In this paper we examine POP generation by relaxing or modifying the action orderings of a sequential plan to o...