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46
Nonlinear programming without a penalty function
 Mathematical Programming
, 2002
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An Algorithmic Framework for GenomeWide Modeling and Analysis of Translation Networks
, 2006
"... ABSTRACT The sequencing of genomes of several organisms and advances in high throughput technologies for transcriptome and proteome analysis has allowed detailed mechanistic studies of transcription and translation using mathematical frameworks that allow integration of both sequencespecific and ki ..."
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ABSTRACT The sequencing of genomes of several organisms and advances in high throughput technologies for transcriptome and proteome analysis has allowed detailed mechanistic studies of transcription and translation using mathematical frameworks that allow integration of both sequencespecific and kinetic properties of these fundamental cellular processes. To understand how perturbations in mRNA levels affect the synthesis of individual proteins within a large protein synthesis network, we consider here a genomescale codonwide model of the translation machinery with explicit description of the processes of initiation, elongation, and termination. The mechanistic codonwide description of the translation process and the large number of mRNAs competing for resources, such as ribosomes, requires the use of novel efficient algorithmic approaches. We have developed such an efficient algorithmic framework for genomescale models of protein synthesis. The mathematical and computational framework was applied to the analysis of the sensitivity of a translation network to perturbation in the rate constants and in the mRNA levels in the system. Our studies suggest that the highest specific protein synthesis rate (protein synthesis rate per mRNA molecule) is achieved when translation is elongationlimited. We find that the mRNA species with the highest number of actively translating ribosomes exerts maximum control on the synthesis of every protein, and the response of protein synthesis rates to mRNA expression variation is a function of the strength of initiation of translation at different mRNA species. Such quantitative understanding of the sensitivity of protein synthesis to the variation of mRNA expression can provide insights into cellular robustness mechanisms and guide the design of protein production systems.
On secondorder optimality conditions for nonlinear programming
 Optimization
"... A new SecondOrder condition is given, which depends on a weak constant rank constraint requirement. We show that practical and publicly available algorithms (www.ime.usp.br/∼egbirgin/tango) of Augmented Lagrangian type converge, after slight modifications, to stationary points defined by the new co ..."
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A new SecondOrder condition is given, which depends on a weak constant rank constraint requirement. We show that practical and publicly available algorithms (www.ime.usp.br/∼egbirgin/tango) of Augmented Lagrangian type converge, after slight modifications, to stationary points defined by the new condition.
A Filter ActiveSet TrustRegion Method
, 2007
"... 2.1 Sequential LinearQuadratic Programming Methods.............. 3 2.2 Difficulties with the LP/TR Step Computation................ 4 ..."
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2.1 Sequential LinearQuadratic Programming Methods.............. 3 2.2 Difficulties with the LP/TR Step Computation................ 4
Conservative Scales in Packing Problems
"... Packing problems (sometimes also called cutting problems) are combinatorial optimization problems concerned with placement of objects (items) in one or several containers. Some packing problems are special cases of several other problems such as resourceconstrained scheduling, capacitated vehicle r ..."
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Packing problems (sometimes also called cutting problems) are combinatorial optimization problems concerned with placement of objects (items) in one or several containers. Some packing problems are special cases of several other problems such as resourceconstrained scheduling, capacitated vehicle routing, etc. In this paper we consider a bounding technique for one and higherdimensional orthogonal packing problems, called conservative scales (CS) (in the scheduling terminology, redundant resources). CS are related to the possible structure of resource consumption: filling of a bin, distribution of the resource to the jobs, etc. In terms of packing, CS are modified item sizes such that the set of feasible packings is not reduced. In fact, every CS represents a valid inequality for a certain binary knapsack polyhedron. CS correspond to dual variables of the setpartitioning model of a special 1D cuttingstock problem. Some CS can be constructed by (datadependent) dualfeasible functions ((D)DFFs). We discuss the relation of CS to DFFs: CS assume that at most 1 copy of each object can appear in a combination, whereas DFFs allow several copies. The literature has investigated socalled extremal maximal DFFs (EMDFFs) which should provide very strong CS. Analogously, we introduce the notions of maximal CS (MCS) and extremal maximal CS (EMCS) and show that EMDFFs do not necessarily produce (E)MCS. We propose fast greedy methods to “maximize ” a given CS. Using the fact that EMCS define facets of the binary knapsack polyhedron, we use lifted cover inequalities as EMCS. For higherdimensional orthogonal packing, we propose a Sequential LP (SLP) method over the set of CS and investigate its convergence. Numerical results are presented.
ON THE CONVERGENCE OF AN ACTIVE SET METHOD FOR ℓ1 MINIMIZATION
"... Abstract. We analyze an abridged version of the activeset algorithm FPC AS proposed in [18] for solving the l1regularized problem, i.e., a weighted sum of the l1norm ‖x‖1 and a smooth function f(x). The active set algorithm alternatively iterates between two stages. In the first “nonmonotone line ..."
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Abstract. We analyze an abridged version of the activeset algorithm FPC AS proposed in [18] for solving the l1regularized problem, i.e., a weighted sum of the l1norm ‖x‖1 and a smooth function f(x). The active set algorithm alternatively iterates between two stages. In the first “nonmonotone line search (NMLS) ” stage, an iterative firstorder method based on “shrinkage” is used to estimate the support at the solution. In the second “subspace optimization ” stage, a smaller smooth problem is solved to recover the magnitudes of the nonzero components of x. We show that NMLS itself is globally convergent and the convergence rate is at least Rlinearly. In particular, NMLS is able to identify of the zero components of a stationary point after a finite number of steps under some mild conditions. The global convergence of FPC AS is established based on the properties
On the Extent of Strategic Voting
, 2012
"... Social scientists have long speculated about individuals’ tendencies to manipulate elections by misrepresenting their preferences. The fact that preference orderings are generally unobserved, however, has made it very difficult to document strategic behavior empirically. Exploiting the incentive str ..."
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Social scientists have long speculated about individuals’ tendencies to manipulate elections by misrepresenting their preferences. The fact that preference orderings are generally unobserved, however, has made it very difficult to document strategic behavior empirically. Exploiting the incentive structure of Germany’s voting system to solve the fundamental identification problem, this paper estimates the extent of strategic voting in large, realworld elections. Evidence from reduced form as well as structural methods indicates that almost one third of voters abandons their most preferred candidate if she is not in contention for victory. As predicted by theory, tactical behavior has a nontrivial impact on individual races. Yet, as one aggregates across districts, these distortions partially offset each other, resulting in considerably more modest effects on the overall distribution of seats.
A Numerical Study of ActiveSet and InteriorPoint Methods for Bound Constrained Optimization ⋆
"... Summary. This papers studies the performance of several interiorpoint and activeset methods on bound constrained optimization problems. The numerical tests show that the sequential linearquadratic programming (SLQP) method is robust, but is not as effective as gradient projection at identifying th ..."
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Summary. This papers studies the performance of several interiorpoint and activeset methods on bound constrained optimization problems. The numerical tests show that the sequential linearquadratic programming (SLQP) method is robust, but is not as effective as gradient projection at identifying the optimal active set. Interiorpoint methods are robust and require a small number of iterations and function evaluations to converge. An analysis of computing times reveals that it is essential to develop improved preconditioners for the conjugate gradient iterations used in SLQP and interiorpoint methods. The paper discusses how to efficiently implement incomplete Cholesky preconditioners and how to eliminate illconditioning caused by the barrier approach. The paper concludes with an evaluation of methods that use quasiNewton approximations to the Hessian of the Lagrangian. 1