Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

On the throughput-WIP trade-off in queueing systems, diminishing returns and the threshold property: A linear programming approach

We present a new unifying framework for investigating throughput-WIP(Work-in-Process) optimal control problems in queueing systems,based on reformulating them as linear programming (LP) problems withspecial structure: We show that if a throughput-WIP performance pairin a stochastic system satisfies the Threshold Property we introducein this paper, then we can reformulate the problem of optimizing alinear objective of throughput-WIP performance as a (semi-infinite)LP problem over a polygon with special structure (a thresholdpolygon). The strong structural properties of such polygones explainthe optimality of threshold policies for optimizing linearperformance objectives: their vertices correspond to the performancepairs of threshold policies. We analyze in this framework theversatile input-output queueing intensity control model introduced byChen and Yao (1990), obtaining a variety of new results, including (a)an exact reformulation of the control problem as an LP problem over athreshold polygon; (b) an analytical characterization of the Min WIPfunction (giving the minimum WIP level required to attain a targetthroughput level); (c) an LP Value Decomposition Theorem that relatesthe objective value under an arbitrary policy with that of a giventhreshold policy (thus revealing the LP interpretation of Chen andYao's optimality conditions); (d) diminishing returns and invarianceproperties of throughput-WIP performance, which underlie thresholdoptimality; (e) a unified treatment of the time-discounted andtime-average cases.

Enrutament i control de flux en xarxes híbrides satèl·lit-terrestre

Les xarxes híbrides satèl·lit-terrestre ofereixen connectivitat a zones remotes i aïllades i permeten resoldre nombrosos problemes de comunicacions. No obstant, presenten diversos reptes, ja que realitzen la comunicació per un canal mòbil terrestre i un canal satèl·lit contigu. Un d'aquests reptes és trobar mecanismes per realitzar eficientment l'enrutament i el control de flux, de manera conjunta. L'objectiu d'aquest projecte és simular i estudiar algorismes existents que resolguin aquests problemes, així com proposar-ne de nous, mitjançant diverses tècniques d'optimització convexa. A partir de les simulacions realitzades en aquest estudi, s'han analitzat àmpliament els diversos problemes d'enrutament i control de flux, i s'han avaluat els resultats obtinguts i les prestacions dels algorismes emprats. En concret, s'han implementat de manera satisfactòria algorismes basats en el mètode de descomposició dual, el mètode de subgradient, el mètode de Newton i el mètode de la barrera logarítmica, entre d'altres, per tal de resoldre els problemes d'enrutament i control de flux plantejats.

Agency problems with non-smooth decision profiles: the case of monopoly under product quality

A method for dealing with monotonicity constraints in optimal control problems is used to generalize some results in the context of monopoly theory, also extending the generalization to a large family of principal-agent programs. Our main conclusion is that many results on diverse economic topics, achieved under assumptions of continuity and piecewise differentiability in connection with the endogenous variables of the problem, still remain valid after replacing such assumptions by two minimal requirements.

Rosca participation in Benin: a commitment issue

In the light of first-hand data from a Beninese urban household survey in Cotonou, we investigate several motives aiming to explain participation in Rotating Savings and Credit Associations. We provide anecdotal pieces of evidence, descriptive statistics, FIML regressions and matching estimates which tend to indicate that most individuals use their participation in a rosca as a device to commit themselves to save money and to deal with self-control problems.

Credit card debt puzzles

Most US credit card holders revolve high-interest debt, often combined with substantial (i) asset accumulation by retirement, and (ii) low-rate liquid assets. Hyperbolic discounting can resolve only the former puzzle (Laibson et al., 2003). Bertaut and Haliassos (2002) proposed an 'accountant-shopper'framework for the latter. The current paper builds, solves, and simulates a fully-specified accountant-shopper model, to show that this framework canactually generate both types of co-existence, as well as target credit card utilization rates consistent with Gross and Souleles (2002). The benchmark model is compared to setups without self-control problems, with alternative mechanisms, and with impatient but fully rational shoppers.

Equities and inequality

Most US credit card holders revolve high-interest debt, often combined with substantial (i) asset accumulation by retirement, and (ii) low-rate liquid assets. Hyperbolic discounting can resolve only the former puzzle (Laibson et al., 2003). Bertaut and Haliassos (2002) proposed an 'accountant-shopper'framework for the latter. The current paper builds, solves, and simulates a fully-specified accountant-shopper model, to show that this framework canactually generate both types of co-existence, as well as target credit card utilization rates consistent with Gross and Souleles (2002). The benchmark model is compared to setups without self-control problems, with alternative mechanisms, and with impatient but fully rational shoppers.

Identifying quantitative operation principles in metabolic pathways: a systematic method for searching feasible enzyme activity patterns leading to cellular adaptive responses

Background: Optimization methods allow designing changes in a system so that specific goals are attained. These techniques are fundamental for metabolic engineering. However, they are not directly applicable for investigating the evolution of metabolic adaptation to environmental changes. Although biological systems have evolved by natural selection and result in well-adapted systems, we can hardly expect that actual metabolic processes are at the theoretical optimum that could result from an optimization analysis. More likely, natural systems are to be found in a feasible region compatible with global physiological requirements. Results: We first present a new method for globally optimizing nonlinear models of metabolic pathways that are based on the Generalized Mass Action (GMA) representation. The optimization task is posed as a nonconvex nonlinear programming (NLP) problem that is solved by an outer- approximation algorithm. This method relies on solving iteratively reduced NLP slave subproblems and mixed-integer linear programming (MILP) master problems that provide valid upper and lower bounds, respectively, on the global solution to the original NLP. The capabilities of this method are illustrated through its application to the anaerobic fermentation pathway in Saccharomyces cerevisiae. We next introduce a method to identify the feasibility parametric regions that allow a system to meet a set of physiological constraints that can be represented in mathematical terms through algebraic equations. This technique is based on applying the outer-approximation based algorithm iteratively over a reduced search space in order to identify regions that contain feasible solutions to the problem and discard others in which no feasible solution exists. As an example, we characterize the feasible enzyme activity changes that are compatible with an appropriate adaptive response of yeast Saccharomyces cerevisiae to heat shock Conclusion: Our results show the utility of the suggested approach for investigating the evolution of adaptive responses to environmental changes. The proposed method can be used in other important applications such as the evaluation of parameter changes that are compatible with health and disease states.

Modelling leaf development in Oxalis latifolia

This study was carried to develop functions that could explain the growth of Oxalis latifolia, in both early stages and throughout the season, contributing to the improvement of its cultural control. Bulbs of the Cornwall form of O. latifolia were buried at 1 and 8 cm in March 1999 and 2000. Samples were destructive at fixed times, and at each time the corresponding BBCH scale codes as well as the absolute number of growing and adult leaves were noted. Using the absolute number of adult leaves (transformed to percentages), a Gaussian curve of three parameters that explains the growth during the season (R2=0.9355) was developed. The BBCH scale permitted the fit of two regression lines that were accurately adjusted for each burial depth (R2=0.9969 and R2=0.9930 respectively for 1 and 8 cm). The best moment for an early defoliation in Northern Spain could be calculated with these regression lines, and was found to be the second week of May. In addition, it was observed that a burial depth of 8 cm does not affect the growing pattern of the weed, but it affects the number of leaves they produce, which decreases to less than a half of those produced at 1 cm.

Incumbent audit firm-provided tax services and the clients with low financial reporting quality

This study investigates whether incumbent audit firm-provided tax services enhance or impair the likelihood of acknowledging client companies’ low financial reporting quality. In particular, we examine the association between tax-related fees and the likelihood of timely restatements, and internal control weakness disclosures among a sample of US companies that all have misstatements in financial information. The empirical findings indicate that companies paying higher tax-related fees are less likely to disclose SOX 404 internal control weakness disclosures, implying that underlying control problems are unacknowledged when incumbent audit firm provided tax-related fees are higher. However, the findings suggest that just providing both audit and tax-related services does not have an impact on audit quality per se, but rather it is the magnitude of the tax-related fees in particular that counts. We also find some evidence suggesting that companies paying higher tax-related fees have higher likelihood of restatement lags, whereas companies paying smaller tax-related fees to their audit firm restate financial statements in a timelier manner. Overall, the findings suggest that audit scrutiny of client companies with low quality financial reporting is weaker when the magnitude of tax-related fees is higher.

Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t & 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions.

Near-linear dynamics in KdV with periodic boundary conditions

Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.

On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

Studies about the atomic capabilities concept for linear control systems in physical multi-agent environments

This paper shows the impact of the atomic capabilities concept to include control-oriented knowledge of linear control systems in the decisions making structure of physical agents. These agents operate in a real environment managing physical objects (e.g. their physical bodies) in coordinated tasks. This approach is presented using an introspective reasoning approach and control theory based on the specific tasks of passing a ball and executing the offside manoeuvre between physical agents in the robotic soccer testbed. Experimental results and conclusions are presented, emphasising the advantages of our approach that improve the multi-agent performance in cooperative systems

The achievable region approach to the optimal control of stochastic systems

The achievable region approach seeks solutions to stochastic optimisation problems by: (i) characterising the space of all possible performances(the achievable region) of the system of interest, and (ii) optimisingthe overall system-wide performance objective over this space. This isradically different from conventional formulations based on dynamicprogramming. The approach is explained with reference to a simpletwo-class queueing system. Powerful new methodologies due to the authorsand co-workers are deployed to analyse a general multiclass queueingsystem with parallel servers and then to develop an approach to optimalload distribution across a network of interconnected stations. Finally,the approach is used for the first time to analyse a class of intensitycontrol problems.