Results 1  10
of
106
R.J.: Interiorpoint methods for nonconvex nonlinear programming: orderings and higherorder methods
 Mathematical Programming Ser. B
, 2000
"... Abstract. In this paper, we present the formulation and solution of optimization problems with complementarity constraints using an interiorpoint method for nonconvex nonlinear programming. We identify possible difficulties that could arise, such as unbounded faces of dual variables, linear depend ..."
Abstract

Cited by 117 (8 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper, we present the formulation and solution of optimization problems with complementarity constraints using an interiorpoint method for nonconvex nonlinear programming. We identify possible difficulties that could arise, such as unbounded faces of dual variables, linear dependence of constraint gradients and initialization issues. We suggest remedies. We include encouraging numerical results on the MacMPEC test suite of problems.
Algorithm 902: GPOPS, A MATLAB Software for Solving MultiplePhase Optimal Control Problems Using the Gauss Pseudospectral Method
, 2010
"... An algorithm is described to solve multiplephase optimal control problems using a recently developed numerical method called the Gauss pseudospectral method. The algorithm is well suited for use in modern vectorized programming languages such as FORTRAN 95 and MATLAB. The algorithm discretizes the ..."
Abstract

Cited by 49 (11 self)
 Add to MetaCart
An algorithm is described to solve multiplephase optimal control problems using a recently developed numerical method called the Gauss pseudospectral method. The algorithm is well suited for use in modern vectorized programming languages such as FORTRAN 95 and MATLAB. The algorithm discretizes the cost functional and the differentialalgebraic equations in each phase of the optimal control problem. The phases are then connected using linkage conditions on the state and time. A largescale nonlinear programming problem (NLP) arises from the discretization and the significant features of the NLP are described in detail. A particular reusable MATLAB implementation of the algorithm, called GPOPS, is applied to three classical optimal control problems to demonstrate its utility. The algorithm described in this article will provide researchers and engineers a useful software tool and a reference when it is desired to implement the Gauss pseudospectral method in other programming languages.
Improving the Numerical Performance of BLP Static and Dynamic Discrete Choice Random Coefficients Demand Estimation,” working paper, the
, 2009
"... Abstract The widelyused estimator of Berry, ..."
Computing optimal strategy against quantal response in security games
 In Proceedings of the Eleventh International Conference on Autonomous Agents and Multiagent Systems (AAMAS
"... To step beyond the firstgeneration deployments of attackerdefender security games – for LAX Police, US FAMS and others – it is critical that we relax the assumption of perfect rationality of the human adversary. Indeed, this assumption is a wellaccepted limitation of classical game theory and mod ..."
Abstract

Cited by 25 (12 self)
 Add to MetaCart
(Show Context)
To step beyond the firstgeneration deployments of attackerdefender security games – for LAX Police, US FAMS and others – it is critical that we relax the assumption of perfect rationality of the human adversary. Indeed, this assumption is a wellaccepted limitation of classical game theory and modeling human adversaries ’ bounded rationality is critical. To this end, quantal response (QR) has provided very promising results to model human bounded rationality. However, in computing optimal defender strategies in realworld security games against a QR model of attackers, we face difficulties including (1) solving a nonlinear nonconvex optimization problem efficiently for massive realworld security games; and (2) addressing constraints on assigning security resources, which adds to the complexity of computing the optimal defender strategy. This paper presents two new algorithms to address these difficulties:
Adaptive Barrier Update Strategies for Nonlinear Interior Methods
, 2005
"... Abstract This paper considers strategies for selecting the barrier parameter at every iterationof an interiorpoint method for nonlinear programming. Numerical experiments suggest that adaptive choices, such as Mehrotra's probing procedure, outperform static strategies that hold the barrier pa ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
(Show Context)
Abstract This paper considers strategies for selecting the barrier parameter at every iterationof an interiorpoint method for nonlinear programming. Numerical experiments suggest that adaptive choices, such as Mehrotra's probing procedure, outperform static strategies that hold the barrier parameter fixed until a barrier optimality test is satisfied. A new adaptive strategy is proposed based on the minimization of a quality function. Thepaper also proposes a globalization framework that ensures the convergence of adaptive interior methods. The barrier update strategies proposed in this paper are applicable to a wide class of interior methods and are tested in the two distinct algorithmic frameworks provided by the ipopt and knitro software packages.
Exploiting Sparsity in Direct Collocation Pseudospectral Methods for Solving Optimal Control Problems
 MarchApril 2012
"... In adirect collocation pseudospectralmethod, a continuoustime optimal control problem is transcribed to afinitedimensional nonlinear programming problem. Solving this nonlinear programming problem as efficiently as possible requires that sparsity at both the first and secondderivative levels be ..."
Abstract

Cited by 10 (9 self)
 Add to MetaCart
(Show Context)
In adirect collocation pseudospectralmethod, a continuoustime optimal control problem is transcribed to afinitedimensional nonlinear programming problem. Solving this nonlinear programming problem as efficiently as possible requires that sparsity at both the first and secondderivative levels be exploited. In this paper, a computationally efficient method is developed for computing the first and second derivatives of the nonlinear programming problem functions arising from a pseudospectral discretization of a continuoustime optimal control problem. Specifically, in this paper, expressions are derived for the objective function gradient, constraint Jacobian, and Lagrangian Hessian arising from the previously developed Radau pseudospectral method. It is shown that the computation of these derivative functions can be reduced to computing the first and second derivatives of the functions in the continuoustime optimal control problem. As a result, the method derived in this paper reduces significantly the amount of computation required to obtain the first and second derivatives required by a nonlinear programming problem solver. The approach derived in this paper is demonstrated on an example where it is found that significant computational benefits are obtained when compared against direct differentiation of the nonlinear programming problem functions. The approach developed in this paper improves the computational efficiency of solving nonlinear programming problems arising from pseudospectral discretizations of continuoustime optimal control problems.
SpinIt: Optimizing moment of inertia for spinnable objects
 ACM Tran. on Graphics (SIGGRAPH
"... We introduce an algorithm for the design of spinning tops and yoyos. Our method optimizes the inertia tensor of an input model by changing its mass distribution, allowing long and stable spins even for complex, asymmetric shapes. Abstract Spinning tops and yoyos have long fascinated cultures arou ..."
Abstract

Cited by 10 (2 self)
 Add to MetaCart
We introduce an algorithm for the design of spinning tops and yoyos. Our method optimizes the inertia tensor of an input model by changing its mass distribution, allowing long and stable spins even for complex, asymmetric shapes. Abstract Spinning tops and yoyos have long fascinated cultures around the world with their unexpected, graceful motions that seemingly elude gravity. We present an algorithm to generate designs for spinning objects by optimizing rotational dynamics properties. As input, the user provides a solid 3D model and a desired axis of rotation. Our approach then modifies the mass distribution such that the principal directions of the moment of inertia align with the target rotation frame. We augment the model by creating voids inside its volume, with interior fill represented by an adaptive multiresolution voxelization. The discrete voxel fill values are optimized using a continuous, nonlinear formulation. Further, we optimize for rotational stability by maximizing the dominant principal moment. We extend our technique to incorporate deformation and multiple materials for cases where internal voids alone are insufficient. Our method is wellsuited for a variety of 3D printed models, ranging from characters to abstract shapes. We demonstrate tops and yoyos that spin surprisingly stably despite their asymmetric appearance.
A Sequential Quadratic Programming Algorithm with an Additional Equality Constrained Phase
, 2008
"... A sequential quadratic programming (SQP) method is presented that aims to overcome some of the drawbacks of contemporary SQP methods. It avoids the difficulties associated with indefinite quadratic programming subproblems by defining this subproblem to be always convex. The novel feature of the appr ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
A sequential quadratic programming (SQP) method is presented that aims to overcome some of the drawbacks of contemporary SQP methods. It avoids the difficulties associated with indefinite quadratic programming subproblems by defining this subproblem to be always convex. The novel feature of the approach is the addition of an equality constrained phase that promotes fast convergence and improves performance in the presence of ill conditioning. This equality constrained phase uses exact second order information and can be implemented using either a direct solve or an iterative method. The paper studies the global and local convergence properties of the new algorithm and presents a set of numerical experiments to illustrate its practical performance.
Local Search Based Evolutionary MultiObjective Optimization Algorithm for Constrained and Unconstrained Problems
, 2009
"... Evolutionary multiobjective optimization algorithms are commonly used to obtain a set of nondominated solutions for over a decade. Recently, a lot of emphasis have been laid on hybridizing evolutionary algorithms with MCDM and mathematical programming algorithms to yield a computationally efficie ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
(Show Context)
Evolutionary multiobjective optimization algorithms are commonly used to obtain a set of nondominated solutions for over a decade. Recently, a lot of emphasis have been laid on hybridizing evolutionary algorithms with MCDM and mathematical programming algorithms to yield a computationally efficient and convergent procedure. In this paper, we test an augmented local search based EMO procedure rigorously on a test suite of constrained and unconstrained multiobjective optimization problems. The success of our approach on most of the test problems not only provides confidence but also stresses the importance of hybrid evolutionary algorithms in solving multiobjective optimization problems.
Competition and Ideological Diversity: Historical Evidence from US Newspapers
, 2012
"... We use data on US newspapers from the early 20th century to study the economic incentives that shape ideological diversity in the media. We show that households prefer likeminded news, and that newspapers seek both to cater to household tastes and to differentiate from their competitors. We estimat ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
We use data on US newspapers from the early 20th century to study the economic incentives that shape ideological diversity in the media. We show that households prefer likeminded news, and that newspapers seek both to cater to household tastes and to differentiate from their competitors. We estimate a model of newspaper demand, entry and political affiliation choice in which newspapers compete for both readers and advertisers. We find that economic competition enhances ideological diversity, that the market undersupplies diversity, and that incorporating the twosidedness of the news market is critical to evaluating the effect of public policy. JEL classification: L11, L52, L82