162 research outputs found
Risk-averse control of undiscounted transient Markov models
We use Markov risk measures to formulate a risk-averse version of the undiscounted total cost problem for a transient controlled Markov process. Using the new concept of a multikernel, we derive conditions for a system to be risk transient, that is, to have finite risk over an infinite time horizon. We derive risk-averse dynamic programming equations satisfied by the optimal policy and we describe methods for solving these equations. We illustrate the results on an optimal stopping problem and an organ transplantation problem. © 2014 Society for Industrial and Applied Mathematic
Computational methods for risk-averse undiscounted transient markov models
The total cost problem for discrete-time controlled transient Markov models is considered. The objective functional is a Markov dynamic risk measure of the total cost. Two solution methods, value and policy iteration, are proposed, and their convergence is analyzed. In the policy iteration method, we propose two algorithms for policy evaluation: the nonsmooth Newton method and convex programming, and we prove their convergence. The results are illustrated on a credit limit control problem. © 2014 INFORMS
Two-stage stochastic minimum s − t cut problems: Formulations, complexity and decomposition algorithms
We introduce the two‐stage stochastic minimum s − t cut problem. Based on a classical linear 0‐1 programming model for the deterministic minimum s − t cut problem, we provide a mathematical programming formulation for the proposed stochastic extension. We show that its constraint matrix loses the total unimodularity property, however, preserves it if the considered graph is a tree. This fact turns out to be not surprising as we prove that the considered problem is NP-hard in general, but admits a linear time solution algorithm when the graph is a tree. We exploit the special structure of the problem and propose a tailored Benders decomposition algorithm. We evaluate the computational efficiency of this algorithm by solving the Benders dual subproblems as max-flow problems. For many tested instances, we outperform a standard Benders decomposition by two orders of magnitude with the Benders decomposition exploiting the max-flow structure of the subproblems
A Look at the Generalized Heron Problem through the Lens of Majorization-Minimization
In a recent issue of this journal, Mordukhovich et al.\ pose and solve an
interesting non-differentiable generalization of the Heron problem in the
framework of modern convex analysis. In the generalized Heron problem one is
given closed convex sets in \Real^d equipped with its Euclidean norm
and asked to find the point in the last set such that the sum of the distances
to the first sets is minimal. In later work the authors generalize the
Heron problem even further, relax its convexity assumptions, study its
theoretical properties, and pursue subgradient algorithms for solving the
convex case. Here, we revisit the original problem solely from the numerical
perspective. By exploiting the majorization-minimization (MM) principle of
computational statistics and rudimentary techniques from differential calculus,
we are able to construct a very fast algorithm for solving the Euclidean
version of the generalized Heron problem.Comment: 21 pages, 3 figure
Processing second-order stochastic dominance models using cutting-plane representations
This is the post-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2011 Springer-VerlagSecond-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczyński (J Bank Finance 30:433–451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541–569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245–269, 2006) for ICCs, and by Künzi-Bay and Mayer (Comput Manage Sci 3:3–27, 2006) for CVaR minimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models. We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541–569, 2006).This study was funded by OTKA, Hungarian
National Fund for Scientific Research, project 47340; by Mobile Innovation Centre, Budapest University of Technology, project 2.2; Optirisk Systems, Uxbridge, UK and by BRIEF (Brunel University Research Innovation and Enterprise Fund)
A Path Algorithm for Constrained Estimation
Many least squares problems involve affine equality and inequality
constraints. Although there are variety of methods for solving such problems,
most statisticians find constrained estimation challenging. The current paper
proposes a new path following algorithm for quadratic programming based on
exact penalization. Similar penalties arise in regularization in model
selection. Classical penalty methods solve a sequence of unconstrained problems
that put greater and greater stress on meeting the constraints. In the limit as
the penalty constant tends to , one recovers the constrained solution.
In the exact penalty method, squared penalties are replaced by absolute value
penalties, and the solution is recovered for a finite value of the penalty
constant. The exact path following method starts at the unconstrained solution
and follows the solution path as the penalty constant increases. In the
process, the solution path hits, slides along, and exits from the various
constraints. Path following in lasso penalized regression, in contrast, starts
with a large value of the penalty constant and works its way downward. In both
settings, inspection of the entire solution path is revealing. Just as with the
lasso and generalized lasso, it is possible to plot the effective degrees of
freedom along the solution path. For a strictly convex quadratic program, the
exact penalty algorithm can be framed entirely in terms of the sweep operator
of regression analysis. A few well chosen examples illustrate the mechanics and
potential of path following.Comment: 26 pages, 5 figure
Respiratory virus type to guide predictive enrichment approaches in the management of the first episode of bronchiolitis: A systematic review
It has become clear that severe bronchiolitis is a heterogeneous disease; even so, current bronchiolitis management guidelines rely on the one-size-fits-all approach regarding achieving both short-term and chronic outcomes. It has been speculated that the use of molecular markers could guide more effective pharmacological management and achieve the prevention of chronic respiratory sequelae. Existing data suggest that asthma-like treatment (systemic corticosteroids and beta2-agonists) in infants with rhinovirus-induced bronchiolitis is associated with improved short-term and chronic outcomes, but robust data is still lacking. We performed a systematic search of PubMed, Embase, Web of Science, and the Cochrane’s Library to identify eligible randomized controlled trials to determine the efficacy of a personalized, virus-dependent application of systemic corticosteroids in children with severe bronchiolitis. Twelve studies with heterogeneous methodology were included. The analysis of the available results comparing the respiratory syncytial virus (RSV)-positive and RSV-negative children did not reveal significant differences in the associatons between systemic corticosteroid use in acute episode and duration of hospitalization (short-term outcome). However, this systematic review identified a trend of the positive association between the use of systematic corticosteroids and duration of hospitalization in RSV-negative infants hospitalized with the first episode of bronchiolitis (two studies). This evidence is not conclusive. Taken together, we suggest the design for future studies to assess the respiratory virus type in guiding predictive enrichment approaches in infants presenting with the first episode of bronchiolitis. </p
Decomposition techniques with mixed integer programming and heuristics for home healthcare planning
We tackle home healthcare planning scenarios in the UK using decomposition methods that incorporate mixed integer programming solvers and heuristics. Home healthcare planning is a difficult problem that integrates aspects from scheduling and routing. Solving real-world size instances of these problems still presents a significant challenge to modern exact optimization solvers. Nevertheless, we propose decomposition techniques to harness the power of such solvers while still offering a practical approach to produce high-quality solutions to real-world problem instances. We first decompose the problem into several smaller sub-problems. Next, mixed integer programming and/or heuristics are used to tackle the sub-problems. Finally, the sub-problem solutions are combined into a single valid solution for the whole problem. The different decomposition methods differ in the way in which subproblems are generated and the way in which conflicting assignments are tackled (i.e. avoided or repaired). We present the results obtained by the proposed decomposition methods and compare them to solutions obtained with other methods. In addition, we conduct a study that reveals how the different steps in the proposed method contribute to those results. The main contribution of this paper is a better understanding of effective ways to combine mixed integer programming within effective decomposition methods to solve real-world instances of home healthcare planning problems in practical computation time
Geometry of Uncertainty Relations for Linear Combinations of Position and Momentum
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by N linear combinations of position and momentum observables. The bounds depend on their degree of incompatibility defined by the area of a parallelogram in an N-dimensional coefficient space. Maximal incompatibility occurs if the observables give rise to regular polygons in phase space. We also conjecture a Hirschman-type uncertainty relation for N observables linear in position and momentum, generalizing the original relation which lower-bounds the sum of the position and momentum Shannon entropies of the particle
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