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Dynamic Portfolio Selection by Augmenting the Asset Space
 THE JOURNAL OF FINANCE • VOL. LXI, NO. 5 • OCTOBER 2006
, 2006
"... We present a novel approach to dynamic portfolio selection that is as easy to implement as the static Markowitz paradigm. We expand the set of assets to include mechanically managed portfolios and optimize statically in this extended asset space. We consider “conditional” portfolios, which invest in ..."
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Cited by 44 (7 self)
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We present a novel approach to dynamic portfolio selection that is as easy to implement as the static Markowitz paradigm. We expand the set of assets to include mechanically managed portfolios and optimize statically in this extended asset space. We consider “conditional” portfolios, which invest in each asset an amount proportional to conditioning variables, and “timing” portfolios, which invest in each asset for a single period and in the riskfree asset for all other periods. The static choice of these managed portfolios represents a dynamic strategy that closely approximates the optimal dynamic strategy for horizons up to 5 years.
User’s Guide for SNOPT Version 7: Software for LargeScale Nonlinear Programming
"... SNOPT is a generalpurpose system for constrained optimization. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for largescale linear and quadratic programming and for linearly constrained optimization, as wel ..."
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Cited by 42 (0 self)
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SNOPT is a generalpurpose system for constrained optimization. It minimizes a linear or nonlinear function subject to bounds on the variables and sparse linear or nonlinear constraints. It is suitable for largescale linear and quadratic programming and for linearly constrained optimization, as well as for general nonlinear programs. SNOPT finds solutions that are locally optimal, and ideally any nonlinear functions should be smooth and users should provide gradients. It is often more widely useful. For example, local optima are often global solutions, and discontinuities in the function gradients can often be tolerated if they are not too close to an optimum. Unknown gradients are estimated by finite differences. SNOPT uses a sequential quadratic programming (SQP) algorithm. Search directions are obtained from QP subproblems that minimize a quadratic model of the Lagrangian function subject to linearized constraints. An augmented Lagrangian merit function is reduced along each search direction to ensure convergence from any starting point.
Optimal gait and form for animal locomotion
 ACM Transactions on Graphics
, 2009
"... We present a fully automatic method for generating gaits and morphologies for legged animal locomotion. Given a specific animal’s shape we can determine an efficient gait with which it can move. Similarly, we can also adapt the animal’s morphology to be optimal for a specific locomotion task. We sho ..."
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Cited by 41 (2 self)
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We present a fully automatic method for generating gaits and morphologies for legged animal locomotion. Given a specific animal’s shape we can determine an efficient gait with which it can move. Similarly, we can also adapt the animal’s morphology to be optimal for a specific locomotion task. We show that determining such gaits is possible without the need to specify a good initial motion, and without manually restricting the allowed gaits of each animal. Our approach is based on a hybrid optimization method which combines an efficient derivativeaware spacetime constraints optimization with a derivativefree approach able to find nonlocal solutions in highdimensional discontinuous spaces. We demonstrate the effectiveness of this approach by synthesizing dynamic locomotions of bipeds, a quadruped, and an imaginary fivelegged creature.
A Pseudospectral Method for the Optimal Control of Constrained Feedback Linearizable Systems
 IEEE Trans. Automat. Contr
"... Abstract—We consider the optimal control of feedback linearizable dynamical systems subject to mixed state and control constraints. In general, a linearizing feedback control does not minimize the cost function. Such problems arise frequently in astronautical applications where stringent performanc ..."
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Cited by 40 (18 self)
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Abstract—We consider the optimal control of feedback linearizable dynamical systems subject to mixed state and control constraints. In general, a linearizing feedback control does not minimize the cost function. Such problems arise frequently in astronautical applications where stringent performance requirements demand optimality over feedback linearizing controls. In this paper, we consider a pseudospectral (PS) method to compute optimal controls. We prove that a sequence of solutions to the PSdiscretized constrained problem converges to the optimal solution of the continuoustime optimal control problem under mild and numerically verifiable conditions. The spectral coefficients of the state trajectories provide a practical method to verify the convergence of the computed solution. The proposed ideas are illustrated by several numerical examples. Index Terms—Constrained optimal control, pseudospectral, nonlinear systems. I.
Efficient numerical methods for nonlinear mpc and moving horizon estimation
, 2008
"... exploitation This overview paper reviews numerical methods for solution of optimal control problems in realtime, as they arise in nonlinear model predictive control (NMPC) as well as in moving horizon estimation (MHE). In the first part, we review numerical optimal control solution methods, focussi ..."
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Cited by 39 (0 self)
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exploitation This overview paper reviews numerical methods for solution of optimal control problems in realtime, as they arise in nonlinear model predictive control (NMPC) as well as in moving horizon estimation (MHE). In the first part, we review numerical optimal control solution methods, focussing exclusively on a discrete time setting. We discuss several algorithmic ”building blocks ” that can be combined to a multitude of algorithms. We start by discussing the sequential and simultaneous approaches, the first leading to smaller, the second to more structured optimization problems. The two big families of Newton type optimization methods, Sequential Quadratic Programming (SQP) and Interior Point (IP) methods, are presented, and we discuss how to exploit the optimal control structure in the solution of the linearquadratic subproblems, where the two major alternatives are “condensing ” and band structure exploiting approaches. The second part of the paper discusses how the algorithms can be adapted to the realtime challenge of NMPC and MHE. We recall an important sensitivity result from parametric optimization, and show that a tangential solution predictor for online data can easily be generated in Newton type algorithms. We point out one important difference between SQP and IP methods: while both methods are able to generate the tangential predictor for fixed active sets, the SQP predictor even works across active set changes. We then classify many proposed realtime optimization approaches from the literature into the developed categories.
Modifying SQP for degenerate problems
 Preprint ANL/MCSP6991097, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill
, 1997
"... Abstract. Most local convergence analyses of the sequential quadratic programming (SQP) algorithm for nonlinear programming make strong assumptions about the solution, namely, that the active constraint gradients are linearly independent and that there are no weakly active constraints. In this paper ..."
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Cited by 39 (6 self)
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Abstract. Most local convergence analyses of the sequential quadratic programming (SQP) algorithm for nonlinear programming make strong assumptions about the solution, namely, that the active constraint gradients are linearly independent and that there are no weakly active constraints. In this paper, we establish a framework for variants of SQP that retain the characteristic superlinear convergence rate even when these assumptions are relaxed, proving general convergence results and placing some recently proposed SQP variants in this framework. We discuss the reasons for which implementations of SQP often continue to exhibit good local convergence behavior even when the assumptions commonly made in the analysis are violated. Finally, we describe a new algorithm that formalizes and extends standard SQP implementation techniques, and we prove convergence results for this method also. AMS subject classifications. 90C33, 90C30, 49M45 1. Introduction. We
MyExperience: A System for
 In Situ Tracing and Capturing of User Feedback on Mobile Phones. Proceedings of MobiSys 2007
, 2007
"... Abstract—With the protiferation of highspeed networks and networked services, prov~loning dfierentiated serviees to a d]verse user base with heterogeneous QoS requirements has beeome an important]problem. The traditional approach of resouree reservation and admiksion control provides both guarantee ..."
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Cited by 38 (10 self)
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Abstract—With the protiferation of highspeed networks and networked services, prov~loning dfierentiated serviees to a d]verse user base with heterogeneous QoS requirements has beeome an important]problem. The traditional approach of resouree reservation and admiksion control provides both guarantees and graded serviee+%however, at the cost of potentially underutilized resources and tindted sealabltity. In thu paper, we describe a WAN QoS prov~]on areMtecture that adaptively organizes beateffort bandwidth into stratified services with graded QoS properties such that the QoS needs of a diverse user base ean be effectively met. Our mdriteetu~BS (Stratitied Besteffort Service)pmmotes a simple user/shnple network reatkation where neither the user nor the network is burdened with complex comprrtationat responsibitities. SBS is scalablq efficient and adaptive, and it complements the guaranteed service archL teeturq sharing a common network substrate comprised of GPS routers. It is also a functional complemen ~ pmvi&oning QoS efficiently commensurate with user needs, albt4t at the cost of weaker pmteetilon. SBS is suited to noncooperative network envimnrnerrts where users belhave seltishly and resouree contention reaohrtion k m~rated by the principle of competitive interaction. A principat feature of SBS is the transformation of usercentric QoS prevision mechanisms—a defining characteristic of competitive interaction entaiting intimate user control of internal networlk rmoureesinto network.eentrie mechanisms while preserving the former’s resouree atloeation
Interior methods for mathematical programs with complementarity constraints
 SIAM J. Optim
, 2004
"... This paper studies theoretical and practical properties of interiorpenalty methods for mathematical programs with complementarity constraints. A framework for implementing these methods is presented, and the need for adaptive penalty update strategies is motivated with examples. The algorithm is sh ..."
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Cited by 36 (10 self)
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This paper studies theoretical and practical properties of interiorpenalty methods for mathematical programs with complementarity constraints. A framework for implementing these methods is presented, and the need for adaptive penalty update strategies is motivated with examples. The algorithm is shown to be globally convergent to strongly stationary points, under standard assumptions. These results are then extended to an interiorrelaxation approach. Superlinear convergence to strongly stationary points is also established. Two strategies for updating the penalty parameter are proposed, and their efficiency and robustness are studied on an extensive collection of test problems.
SQP Methods And Their Application To Numerical Optimal Control
, 1997
"... . In recent years, generalpurpose sequential quadratic programming (SQP) methods have been developed that can reliably solve constrained optimization problems with many hundreds of variables and constraints. These methods require remarkably few evaluations of the problem functions and can be shown ..."
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Cited by 36 (0 self)
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. In recent years, generalpurpose sequential quadratic programming (SQP) methods have been developed that can reliably solve constrained optimization problems with many hundreds of variables and constraints. These methods require remarkably few evaluations of the problem functions and can be shown to converge to a solution under very mild conditions on the problem. Some practical and theoretical aspects of applying generalpurpose SQP methods to optimal control problems are discussed, including the influence of the problem discretization and the zero/nonzero structure of the problem derivatives. We conclude with some recent approaches that tailor the SQP method to the control problem. Key words. largescale optimization, sequential quadratic programming (SQP) methods, optimal control problems, multiple shooting methods, single shooting methods, collocation methods AMS subject classifications. 49J20, 49J15, 49M37, 49D37, 65F05, 65K05, 90C30 1. Introduction. Recently there has been c...
Disciplined convex programming
 Global Optimization: From Theory to Implementation, Nonconvex Optimization and Its Application Series
, 2006
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