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599
On Augmented Lagrangian methods with general lowerlevel constraints
, 2005
"... Augmented Lagrangian methods with general lowerlevel constraints are considered in the present research. These methods are useful when efficient algorithms exist for solving subproblems where the constraints are only of the lowerlevel type. Two methods of this class are introduced and analyzed. In ..."
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Cited by 84 (7 self)
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Augmented Lagrangian methods with general lowerlevel constraints are considered in the present research. These methods are useful when efficient algorithms exist for solving subproblems where the constraints are only of the lowerlevel type. Two methods of this class are introduced and analyzed. Inexact resolution of the lowerlevel constrained subproblems is considered. Global convergence is proved using the Constant Positive Linear Dependence constraint qualification. Conditions for boundedness of the penalty parameters are discussed. The reliability of the approach is tested by means of an exhaustive comparison against Lancelot. All the problems of the Cute collection are used in this comparison. Moreover, the resolution of location problems in which many constraints of the lowerlevel set are nonlinear is addressed, employing the Spectral Projected Gradient method for solving the subproblems. Problems of this type with more than 3 × 10 6 variables and 14 × 10 6 constraints are solved in this way, using moderate computer time.
Local convergence of SQP methods for Mathematical Programs with Equilibrium Constraints
, 2002
"... Recently, it has been shown that Nonlinear Programming solvers can successfully solve a range of Mathematical Programs with Equilibrium Constraints (MPECs). ..."
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Cited by 72 (19 self)
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Recently, it has been shown that Nonlinear Programming solvers can successfully solve a range of Mathematical Programs with Equilibrium Constraints (MPECs).
LQRTrees: Feedback motion planning via sums of squares verification
 International Journal of Robotics Research
, 2010
"... Advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of attraction for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses rigorously computed stability regions to build a sparse tree ..."
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Cited by 68 (21 self)
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Advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of attraction for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses rigorously computed stability regions to build a sparse tree of LQRstabilized trajectories. The region of attraction of this nonlinear feedback policy “probabilistically covers ” the entire controllable subset of the state space, verifying that all initial conditions that are capable of reaching the goal will reach the goal. We numerically investigate the properties of this systematic nonlinear feedback design algorithm on simple nonlinear systems, prove the property of probabilistic coverage, and discuss extensions and implementation details of the basic algorithm. 1
Coordinating Multiple Robots with Kinodynamic Constraints along Specified Paths
, 2005
"... This paper focuses on the collisionfree coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize t ..."
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Cited by 68 (9 self)
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This paper focuses on the collisionfree coordination of multiple robots with kinodynamic constraints along specified paths. We present an approach to generate continuous velocity profiles for multiple robots; these velocity profiles satisfy the dynamics constraints, avoid collisions, and minimize the completion time. The approach, which combines techniques from optimal control and mathematical programming, consists of identifying collision segments along each robot's path, and then optimizing the robots' velocities along the collision and collisionfree segments. First, for each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding twopoint boundary value problems. The collision avoidance constraints for pairs of robots can then be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations, which provide schedules that give lower and upper bounds on the optimum; the upper bound schedule is designed to provide continuous velocity trajectories that are feasible. The approach is illustrated with coordination of multiple robots, modeled as double integrators subject to velocity and acceleration constraints. An application to coordination of nonholonomic carlike robots is described, along with implementation results for 12 robots.
Computer optimization of a minimal biped model discovers walking and running
 Nature
, 2005
"... Note: This is a “preprint ” version of the paper published in Nature. It is wordforword the same as the published version, except where noted explicitly as footnotes. Five minor typographical errors in the published version have been corrected in this version, as also a small error in Figure 3. ..."
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Cited by 67 (6 self)
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Note: This is a “preprint ” version of the paper published in Nature. It is wordforword the same as the published version, except where noted explicitly as footnotes. Five minor typographical errors in the published version have been corrected in this version, as also a small error in Figure 3. None of the conclusions of the paper are affected by these changes. Although people’s legs are capable of a broad range of muscleuse and gait patterns, they generally prefer just two. They walk, swinging their body over a relatively straight leg with each step, or run, bouncing up off a bent leg between aerial phases. Walking feels easiest when going slowly, and running feels easiest when going faster. More unusual gaits seem more tiring. Perhaps this is because walking and running use the least energy [1; 2; 3; 4; 5; 6; 7]. Addressing this classic [1] conjecture with experiments [2; 3] requires comparing walking and
An interior point algorithm for largescale nonlinear . . .
, 2002
"... Nonlinear programming (NLP) has become an essential tool in process engineering, leading to prot gains through improved plant designs and better control strategies. The rapid advance in computer technology enables engineers to consider increasingly complex systems, where existing optimization codes ..."
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Cited by 64 (3 self)
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Nonlinear programming (NLP) has become an essential tool in process engineering, leading to prot gains through improved plant designs and better control strategies. The rapid advance in computer technology enables engineers to consider increasingly complex systems, where existing optimization codes reach their practical limits. The objective of this dissertation is the design, analysis, implementation, and evaluation of a new NLP algorithm that is able to overcome the current bottlenecks, particularly in the area of process engineering. The proposed algorithm follows an interior point approach, thereby avoiding the combinatorial complexity of identifying the active constraints. Emphasis is laid on exibility in the computation of search directions, which allows the tailoring of the method to individual applications and is mandatory for the solution of very large problems. In a fullspace version the method can be used as general purpose NLP solver, for example in modeling environments such as Ampl. The reduced space version, based on coordinate decomposition, makes it possible to tailor linear algebra
On the solution of equality constrained quadratic programming problems arising . . .
, 1998
"... ..."
Momentumbased Parameterization of Dynamic Character Motion
, 2004
"... This paper presents a system for rapid editing of highly dynamic motion capture data. At the heart of this system is an optimization algorithm that can transform the captured motion so that it satisfies highlevel user constraints while enforcing that the linear and angular momentum of the motion ..."
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Cited by 52 (2 self)
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This paper presents a system for rapid editing of highly dynamic motion capture data. At the heart of this system is an optimization algorithm that can transform the captured motion so that it satisfies highlevel user constraints while enforcing that the linear and angular momentum of the motion remain physically plausible. Unlike most previous approaches to motion editing, our algorithm does not require pose specification or model reduction, and the user only need specify highlevel changes to the input motion. To preserve the dynamic behavior of the input motion, we introduce a splinebased parameterization that matches the linear and angular momentum patterns of the motion capture data. Because our algorithm enables rapid convergence by presenting a good initial state of the optimization, the user can efficiently generate a large number of realistic motions from a single input motion. The algorithm
On the implementation of an algorithm for largescale equality constrained optimization
 SIAM Journal on Optimization
, 1998
"... Abstract. This paper describes a software implementation of Byrd and Omojokun’s trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques ..."
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Cited by 49 (12 self)
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Abstract. This paper describes a software implementation of Byrd and Omojokun’s trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques for solving the subproblems occurring in the algorithm. Second derivative information can be used, but when it is not available, limited memory quasiNewton approximations are made. The performance of the code is studied using a set of difficult test problems from the CUTE collection.
An Algorithm for Nonlinear Optimization Using Linear Programming and Equality Constrained Subproblems
, 2003
"... This paper describes an activeset algorithm for largescale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the activ ..."
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Cited by 49 (13 self)
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This paper describes an activeset algorithm for largescale nonlinear programming based on the successive linear programming method proposed by Fletcher and Sainz de la Maza [10]. The step computation is performed in two stages. In the first stage a linear program is solved to estimate the active set at the solution. The linear program is obtained by making a linear approximation to the ` 1 penalty function inside a trust region. In the second stage, an equality constrained quadratic program (EQP) is solved involving only those constraints that are active at the solution of the linear program.