Results 1  10
of
22
An approximate dynamic programming approach to network revenue management with customer choice. Transportation Science, 43:381–394, 2009. Use of Approximate Dynamic Programming for Production Optimization SPE 141677 (a) Comparison with baseline strategy (
"... We consider a network revenue management problem where customers choose among open fare products according to some prespecified choice model. Starting with a Markov decision process (MDP) formulation, we approximate the value function with an affine function of the state vector. We show that the re ..."
Abstract

Cited by 22 (0 self)
 Add to MetaCart
We consider a network revenue management problem where customers choose among open fare products according to some prespecified choice model. Starting with a Markov decision process (MDP) formulation, we approximate the value function with an affine function of the state vector. We show that the resulting problem provides a tighter bound for the MDP value than the choicebased linear program proposed by Gallego et al. (2004) and Liu and van Ryzin (2007). We develop a column generation algorithm to solve the problem for a multinomial logit choice model with disjoint consideration sets. We also derive a bound as a byproduct of a decomposition heuristic. Our numerical study shows the policies from our solution approach can significantly outperform heuristics from the choicebased linear program. While a substantial amount of research has been done on methods for solving the network revenue management problem, much less work has been done in solving the version where customers choose among available network products. Usually, when airlines open up a menu of fares for a given set of flights, customers will make substitutions between those available, or purchase nothing. Although incorporating customer choice is important in practice, methodologically it is
REFORMULATIONS IN MATHEMATICAL PROGRAMMING: DEFINITIONS AND SYSTEMATICS
, 2008
"... A reformulation of a mathematical program is a formulation which shares some properties with, but is in some sense better than, the original program. Reformulations are important with respect to the choice and efficiency of the solution algorithms; furthermore, it is desirable that reformulations c ..."
Abstract

Cited by 19 (14 self)
 Add to MetaCart
A reformulation of a mathematical program is a formulation which shares some properties with, but is in some sense better than, the original program. Reformulations are important with respect to the choice and efficiency of the solution algorithms; furthermore, it is desirable that reformulations can be carried out automatically. Reformulation techniques are very common in mathematical programming but interestingly they have never been studied under a common framework. This paper attempts to move some steps in this direction. We define a framework for storing and manipulating mathematical programming formulations, give several fundamental definitions categorizing reformulations in essentially four types (optreformulations, narrowings, relaxations and approximations). We establish some theoretical results and give reformulation examples for each type.
Reformulations in Mathematical Programming: A Computational Approach
"... Summary. Mathematical programming is a language for describing optimization problems; it is based on parameters, decision variables, objective function(s) subject to various types of constraints. The present treatment is concerned with the case when objective(s) and constraints are algebraic mathema ..."
Abstract

Cited by 18 (13 self)
 Add to MetaCart
Summary. Mathematical programming is a language for describing optimization problems; it is based on parameters, decision variables, objective function(s) subject to various types of constraints. The present treatment is concerned with the case when objective(s) and constraints are algebraic mathematical expressions of the parameters and decision variables, and therefore excludes optimization of blackbox functions. A reformulation of a mathematical program P is a mathematical program Q obtained from P via symbolic transformations applied to the sets of variables, objectives and constraints. We present a survey of existing reformulations interpreted along these lines, some example applications, and describe the implementation of a software framework for reformulation and optimization. 1
Improved total variationtype regularization using higherorder edge detectors
 SIAM Journal on Imaging Sciences
"... Abstract. We present a novel deconvolution approach to accurately restore piecewise smooth signals from blurred data. The first stage uses Higher Order Total Variation restorations to obtain an estimate of the location of jump discontinuities from the blurred data. In the second stage the estimated ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
Abstract. We present a novel deconvolution approach to accurately restore piecewise smooth signals from blurred data. The first stage uses Higher Order Total Variation restorations to obtain an estimate of the location of jump discontinuities from the blurred data. In the second stage the estimated jump locations are used to determine the local orders of a Variable Order Total Variation restoration. The method replaces the first order derivative approximation used in standard Total Variation by a variable order derivative operator. Smooth segments as well as jump discontinuities are restored while the staircase effect typical for standard first order Total Variation regularization is avoided. As compared to first order Total Variation, signal restorations are more accurate representations of the true signal, as measured in a relative l 2 norm. The method can also be used to obtain an accurate estimation of the locations and sizes of the true jump discontinuities. The approach is independent of the algorithm used for the standard Total Variation problem and is, consequently, readily incorporated in existing Total Variation restoration codes.
On Reoptimizing MultiClass Classifiers ∗
, 2006
"... Significant changes in the instance distribution or associated cost function of a learning problem require one to reoptimize a previously learned classifier to work under new conditions. We study the problem of reoptimizing a multiclass classifier based on its ROC hypersurface and a matrix describi ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Significant changes in the instance distribution or associated cost function of a learning problem require one to reoptimize a previously learned classifier to work under new conditions. We study the problem of reoptimizing a multiclass classifier based on its ROC hypersurface and a matrix describing the costs of each type of prediction error. For a binary classifier, it is straightforward to find an optimal operating point based on its ROC curve and the relative cost of true positive to false positive error. However, the corresponding multiclass problem (finding an optimal operating point based on a ROC hypersurface and cost matrix) is more challenging and until now, it was unknown whether an efficient algorithm existed that found an optimal solution. We answer this question by first proving that the decision version of this problem is NPcomplete. As a complementary positive result, we give an algorithm that finds an optimal solution in polynomial time if the number of classes n is a constant. We also present several heuristics for this problem, including linear, nonlinear, and quadratic programming formulations, genetic algorithms, and a customized algorithm. Empirical results suggest that under uniform costs several methods exhibit significant improvements while genetic algorithms and margin maximization quadratic programs fare the best under nonuniform cost models.
Optimisation of contribution of candidate parents to maximise genetic gain and restricting inbreeding using semidefinite programming
, 2006
"... ..."
An Algorithm for Unconstrained Quadratically Penalized Convex Optimization
, 811
"... A descent algorithm, “QuasiQuadratic Minimization with Memory” (QQMM), is proposed for unconstrained minimization of the sum, F, of a nonnegative convex function, V, and a quadratic form. Such problems come up in regularized estimation in machine learning and statistics. In addition to values of F ..."
Abstract
 Add to MetaCart
A descent algorithm, “QuasiQuadratic Minimization with Memory” (QQMM), is proposed for unconstrained minimization of the sum, F, of a nonnegative convex function, V, and a quadratic form. Such problems come up in regularized estimation in machine learning and statistics. In addition to values of F, QQMM requires the (sub)gradient of V. Two features of QQMM help keep low the number of evaluations of the objective function it needs. First, QQMM provides good control over stopping the iterative search. This feature makes QQMM well adapted to statistical problems because in such problems the objective function is based on random data and therefore stopping early is sensible. Secondly, QQMM uses a complex method for determining trial minimizers of F. After a description of the problem and algorithm a simulation study comparing QQMM to the popular BFGS optimization algorithm is described. The simulation study and other experiments suggest that QQMM is generally substantially faster than BFGS in the problem domain for which it was designed. A QQMMBFGS hybrid is also generally substantially faster than BFGS but does better than QQMM when QQMM is very slow.
RealTime Convex Optimization . . .  Recent advances that make it easier to design and implement algorithms
, 2010
"... Convex optimization has been used in signal processing for a long time to choose coefficients for use in fast (linear) algorithms, such as in filter or array design; more recently, it has been used to carry out (nonlinear) processing on the signal itself. Examples of the latter case include total va ..."
Abstract
 Add to MetaCart
Convex optimization has been used in signal processing for a long time to choose coefficients for use in fast (linear) algorithms, such as in filter or array design; more recently, it has been used to carry out (nonlinear) processing on the signal itself. Examples of the latter case include total variation denoising, compressed sensing, fault detection, and image classification. In both scenarios, the optimization is carried out on time scales of seconds or minutes and without strict time constraints. Convex optimization has traditionally been considered computationally expensive, so its use has been limited to applications where plenty of time is available. Such restrictions are no longer justified. The combination of dramatically increased computing power, modern algorithms, and new coding approaches has delivered an enormous speed increase, which makes it possible to solve modestsized convex optimization problems on microsecond or millisecond time scales and with strict deadlines. This enables realtime convex optimization in signal processing.
Robust counterparts of . . .
"... Of interest here are linear data fitting problems with uncertain data which lie in a given uncertainty set. A robust counterpart of such a problem may be interpreted as the problem of finding a solution which is best over all possible perturbations of the data which lie in the set. In particular, ro ..."
Abstract
 Add to MetaCart
Of interest here are linear data fitting problems with uncertain data which lie in a given uncertainty set. A robust counterpart of such a problem may be interpreted as the problem of finding a solution which is best over all possible perturbations of the data which lie in the set. In particular, robust counterparts of total least squares problems have been studied and good algorithms are available. The purpose of this paper is to consider robust counterparts of the problems considered as errorsinvariables problems, when it is appropriate to work directly with the uncertain variable values. It is shown how the original problems can be replaced by convex optimization problems in fewer variables for which standard software may be applied.
cvx Users ’ Guide for cvx version 1.22 ∗
, 2012
"... 1.1 What is cvx?............................... 4 1.2 What is disciplined convex programming?............... 5 1.3 About this version............................ 5 ..."
Abstract
 Add to MetaCart
1.1 What is cvx?............................... 4 1.2 What is disciplined convex programming?............... 5 1.3 About this version............................ 5