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32
The Response of Drug Expenditures to NonLinear Contract Design: Evidence from Medicare Part D
 NBER Working Paper No. 19393, National Bureau of Economic Research
, 2013
"... Abstract. We study the demand response to nonlinear price schedules using data on insurance contracts and prescription drug purchases in Medicare Part D. We exploit the kink in individualsbudget set created by the famous donut hole,where insurance becomes discontinuously much less generous on the m ..."
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Cited by 12 (3 self)
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Abstract. We study the demand response to nonlinear price schedules using data on insurance contracts and prescription drug purchases in Medicare Part D. We exploit the kink in individualsbudget set created by the famous donut hole,where insurance becomes discontinuously much less generous on the margin, to provide descriptive evidence of the drug purchase response to a price increase. We then specify and estimate a simple dynamic model of drug use that allows us to quantify the spending response along the entire nonlinear budget set. We use the model for counterfactual analysis of the increase in spending from
llingthe donut hole, as will be required by 2020 under the A¤ordable Care Act. In our baseline model, which considers spending decisions within a single year, we estimate that
llingthe donut hole will increase annual drug spending by about $150, or about 8 percent. About onequarter of this spending increase reects anticipatorybehavior, coming from bene
ciaries whose spending prior to the policy change would leave them short of reaching the donut hole. We also present descriptive evidence of crossyear substitution of spending by individuals who reach the kink, which motivates a simple extension to our baseline model that allows in a highly stylized way for individuals to engage in such cross year substitution. Our estimates from this extension suggest that a large share of the $150 drug spending increase could be attributed to crossyear substitution, and the net increase could be as little as $45 per year.
Smoothing and WorstCase Complexity for DirectSearch Methods in Nonsmooth Optimization
, 2012
"... In the context of the derivativefree optimization of a smooth objective function, it has been shown that the worst case complexity of directsearch methods is of the same order as the one of steepest descent for derivativebased optimization, more precisely that the number of iterations needed to r ..."
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Cited by 8 (2 self)
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In the context of the derivativefree optimization of a smooth objective function, it has been shown that the worst case complexity of directsearch methods is of the same order as the one of steepest descent for derivativebased optimization, more precisely that the number of iterations needed to reduce the norm of the gradient of the objective function below a certain threshold is proportional to the inverse of the threshold squared. Motivated by the lack of such a result in the nonsmooth case, we propose, analyze, and test a class of smoothing directsearch methods for the unconstrained optimization of nonsmooth functions. Given a parameterized family of smoothing functions for the nonsmooth objective function dependent on a smoothing parameter, this class of methods consists of applying a directsearch algorithm for a fixed value of the smoothing parameter until the step size is relatively small, after which the smoothing parameter is reduced and the process is repeated. One can show that the worst case complexity (or cost) of this procedure is roughly one order of magnitude worse than the one for direct search or steepest descent on smooth functions. The class of smoothing directsearch methods is also showed to enjoy asymptotic global convergence properties. Some preliminary numerical experiments indicates that this approach leads to better values of the objective function, pushing in some cases the optimization further, apparently without an additional cost in the number of function evaluations.
TaskRelevant Roadmaps: A Framework for Humanoid Motion Planning
"... Abstract — We introduce a novel framework that builds taskrelevant roadmaps (TRMs). TRMs can be used to plan complex taskrelevant motions on robots with many degrees of freedom. To this end we create a new sampling based inverse kinematics optimizer called Natural Gradient Inverse Kinematics (NGIK) ..."
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Cited by 4 (4 self)
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Abstract — We introduce a novel framework that builds taskrelevant roadmaps (TRMs). TRMs can be used to plan complex taskrelevant motions on robots with many degrees of freedom. To this end we create a new sampling based inverse kinematics optimizer called Natural Gradient Inverse Kinematics (NGIK), based on the principled heuristic solver called natural evolution strategies (NES). We build TRMs using a construction algorithm that iteratively optimizes postures using NGIK that cover an arbitrary taskspace. NGIK can express constraints with arbitrary costfunctions and thus can transparently deal with hard and soft constraints. The construction algorithm can express the taskspace by arbitrary taskfunctions and grows the TRM to maximally cover the taskspace while minimizing the constraints. These properties make the framework very flexible while still handling complex movements in robots with high degrees of freedom. We show NGIK outperforms recent algorithms in this domain and show the effectiveness of our method on the iCub robot, using the 41 DOF of its full upper body, arms, hands, head, and eyes. A videodemo shows TRMs applied on real robotic tasks on the iCub humanoid
Blackbox optimization benchmarking of the GLOBAL method
"... GLOBAL is a multistart type stochastic method for bound constrained global optimization problems. Its goal is to find the best local minima that are potentially global. For this reason it involves a combination of sampling, clustering, and local search. The role of clustering is to reduce the number ..."
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Cited by 2 (1 self)
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GLOBAL is a multistart type stochastic method for bound constrained global optimization problems. Its goal is to find the best local minima that are potentially global. For this reason it involves a combination of sampling, clustering, and local search. The role of clustering is to reduce the number of local searches by forming groups of points around the local minimizers from a uniform sampled domain and to start few local searches in each of those groups. We evaluate the performance of the GLOBAL algorithm on the BBOB2009 noiseless testbed, containing problems which reflect the typical difficulties arising in realword applications. The results show that up to a small function evaluation budget, GLOBAL performs well. We improved the parametrization of it and compared the performance with the MATLAB R2010a GlobalSearch algorithm on the BBOB2010 noiseless testbed between dimensions 2 and 20. According to the results the studied methods perform similar.
A class of derivativefree nonmonotone optimization algorithms employing coordinate rotations and gradient approximations
 Computational Optimization and Applications
"... Abstract In this paper we study a class of derivativefree unconstrained minimization algorithms employing nonmonotone inexact linesearch techniques along a set of suitable search directions. In particular, we define globally convergent nonmonotone versions of some wellknown derivativefree methods ..."
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Abstract In this paper we study a class of derivativefree unconstrained minimization algorithms employing nonmonotone inexact linesearch techniques along a set of suitable search directions. In particular, we define globally convergent nonmonotone versions of some wellknown derivativefree methods and we propose a new algorithm combining coordinate rotations with approximate simplex gradients. Through extensive numerical experimentation, we show that the proposed algorithm is highly competitive in comparison with some of the most efficient direct search methods and model based methods on a large set of test problems.
Globally convergent evolution strategies for constrained optimization
 Comput. Optim. Appl
, 2015
"... Abstract In this paper we propose, analyze, and test algorithms for linearly constrained optimization when no use of derivatives of the objective function is made. The proposed methodology is built upon the globally convergent evolution strategies previously introduced by the authors for unconstrai ..."
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Abstract In this paper we propose, analyze, and test algorithms for linearly constrained optimization when no use of derivatives of the objective function is made. The proposed methodology is built upon the globally convergent evolution strategies previously introduced by the authors for unconstrained optimization. Two approaches are encompassed to handle the constraints. In a first approach, feasibility is first enforced by a barrier function and the objective function is then evaluated directly at the feasible generated points. A second approach projects first all the generated points onto the feasible domain before evaluating the objective function. The resulting algorithms enjoy favorable global convergence properties (convergence to stationarity from arbitrary starting points), regardless of the linearity of the constraints. The algorithmic implementation (i) includes a step where previously evaluated points are used to accelerate the search (by minimizing quadratic models) and (ii) addresses general linearly constrained optimization. Our solver is compared to others, and the numerical results confirm its competitiveness in terms of efficiency and robustness.
UNCLASSIFIED An Advanced Computational Approach to System of Systems Analysis & Architecting Using AgentBased Behavioral Model
, 2013
"... Report Documentation Page Form ApprovedOMB No. 07040188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing an ..."
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Report Documentation Page Form ApprovedOMB No. 07040188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 222024302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE
General solution methods for mixed integer . . .
, 2013
"... In a number of situations the derivative of the objective function of an optimization problem is not available. This thesis presents a novel algorithm for solving mixed integer programs when this is the case. The algorithm is the first developed for problems of this type which uses a trust region ..."
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In a number of situations the derivative of the objective function of an optimization problem is not available. This thesis presents a novel algorithm for solving mixed integer programs when this is the case. The algorithm is the first developed for problems of this type which uses a trust region methodology. Three implementations of the algorithm are developed and deterministic proofs of convergence to local minima are provided for two of the implementations. In the development of the algorithm several other contributions are made. The derivative free algorithm requires the solution of several mixed integer quadratic programming subproblems and novel methods for solving nonconvex instances of these problems are developed in this thesis. Additionally, it is shown that the current definitions of local minima for mixed integer pro