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60
Interiorpoint methods for nonconvex nonlinear programming: Filter methods and merit functions
 Computational Optimization and Applications
, 2002
"... Abstract. In this paper, we present global and local convergence results for an interiorpoint method for nonlinear programming and analyze the computational performance of its implementation. The algorithm uses an ℓ1 penalty approach to relax all constraints, to provide regularization, and to bound ..."
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Cited by 84 (7 self)
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Abstract. In this paper, we present global and local convergence results for an interiorpoint method for nonlinear programming and analyze the computational performance of its implementation. The algorithm uses an ℓ1 penalty approach to relax all constraints, to provide regularization, and to bound the Lagrange multipliers. The penalty problems are solved using a simplified version of Chen and Goldfarb’s strictly feasible interiorpoint method [12]. The global convergence of the algorithm is proved under mild assumptions, and local analysis shows that it converges Qquadratically for a large class of problems. The proposed approach is the first to simultaneously have all of the following properties while solving a general nonconvex nonlinear programming problem: (1) the convergence analysis does not assume boundedness of dual iterates, (2) local convergence does not require the Linear Independence Constraint Qualification, (3) the solution of the penalty problem is shown to locally converge to optima that may not satisfy the KarushKuhnTucker conditions, and (4) the algorithm is applicable to mathematical programs with equilibrium constraints. Numerical testing on a set of general nonlinear programming problems, including degenerate problems and infeasible problems, confirm the theoretical results. We also provide comparisons to a highlyefficient nonlinear solver and thoroughly analyze the effects of enforcing theoretical convergence guarantees on the computational performance of the algorithm. 1.
CUTEr (and SifDec), a constrained and unconstrained testing environment, revisited
 ACM Transactions on Mathematical Software
, 2001
"... Abstract. The initial release of CUTE, a widely used testing environment for optimization software was described in [2]. The latest version, now known as CUTEr is presented. New features include reorganisation of the environment to allow simultaneous multiplatform installation, new tools for, and i ..."
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Cited by 53 (2 self)
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Abstract. The initial release of CUTE, a widely used testing environment for optimization software was described in [2]. The latest version, now known as CUTEr is presented. New features include reorganisation of the environment to allow simultaneous multiplatform installation, new tools for, and interfaces to, optimization packages, and a considerably simplified and entirely automated installation procedure for unix systems. The SIF decoder, which used to be a part of CUTE, has become a separate tool, easily callable by various packages. It features simple extensions to the SIF test problem format and the generation of files suited to automatic differentiation packages. Key words. Nonlinear constrained optimization, testing environment, shared filesystems, heterogeneous environment, SIF format 1.
On Solving Mathematical Programs With Complementarity Constraints As Nonlinear Programs
, 2002
"... . We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using classical algorithms and procedures from nonlinear programming. Although MPCCs do not satisfy a constraint qualification, we establish sufficient conditions for their Lagrange multiplier ..."
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Cited by 33 (2 self)
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. We investigate the possibility of solving mathematical programs with complementarity constraints (MPCCs) using classical algorithms and procedures from nonlinear programming. Although MPCCs do not satisfy a constraint qualification, we establish sufficient conditions for their Lagrange multiplier set to be nonempty in two different formulations. MPCCs that have nonempty Lagrange multiplier sets and that satisfy the quadratic growth condition can be approached by the elastic mode with a boundedpenalty parameter. This transformsthe MPCC into a nonlinear program with additional variables that has an isolated stationary point and local minimum at the solution of the original problem, which in turn makes it approachable by a sequential quadratic programming algorithm. The robustness of the elastic mode when applied to MPCCs is demonstrated by several numerical examples. 1. Introduction. Complementarity constraints can be used to model numerous economics or mechanics applications [18, 25]....
A globally convergent linearly constrained Lagrangian method for nonlinear optimization
 SIAM J. Optim
, 2002
"... Abstract. For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form “minimize an augmented Lagrangian function subject to linearized constraints. ” Such methods converge rapidly near a solution but may not be relia ..."
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Cited by 22 (5 self)
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Abstract. For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form “minimize an augmented Lagrangian function subject to linearized constraints. ” Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. Nevertheless, the wellknown software package MINOS has proved effective on many large problems. Its success motivates us to derive a related LCL algorithm that possesses three important properties: it is globally convergent, the subproblem constraints are always feasible, and the subproblems may be solved inexactly. The new algorithm has been implemented in Matlab, with an option to use either MINOS or SNOPT (Fortran codes) to solve the linearly constrained subproblems. Only first derivatives are required. We present numerical results on a subset of the COPS, HS, and CUTE test problems, which include many large examples. The results demonstrate the robustness and efficiency of the stabilized LCL procedure.
Degenerate Nonlinear Programming with a Quadratic Growth Condition
 Preprint ANL/MCSP7610699, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, Ill
"... . We show that the quadratic growth condition and the MangasarianFromovitz constraint qualification imply that local minima of nonlinear programs are isolated stationary points. As a result, when started sufficiently close to such points, an L1 exact penalty sequential quadratic programming algorit ..."
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Cited by 20 (6 self)
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. We show that the quadratic growth condition and the MangasarianFromovitz constraint qualification imply that local minima of nonlinear programs are isolated stationary points. As a result, when started sufficiently close to such points, an L1 exact penalty sequential quadratic programming algorithm will induce at least Rlinear convergence of the iterates to such a local minimum. We construct an example of a degenerate nonlinear program with a unique local minimum satisfying the quadratic growth and the MangasarianFromovitz constraint qualification but for which no positive semidefinite augmented Lagrangian exists. We present numerical results obtained using several nonlinear programming packages on this example, and discuss its implications for some algorithms. 1. Introduction. Recently, there has been renewed interest in analyzing and modifying sequential quadratic programming (SQP) algorithms for constrained nonlinear optimization for cases where the traditional regularity cond...
CPR: Mixed Task and Data Parallel Scheduling for Distributed Systems
 In Proceedings of the 15th International Parallel and Distributed Symposium
, 2001
"... It is wellknown that mixing task and data parallelism to solve large computational applications often yields better speedups compared to either applying pure task parallelism or pure data parallelism. Typically, the applications are modeled in terms of a dependence graph of coarsegrain dataparall ..."
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Cited by 17 (6 self)
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It is wellknown that mixing task and data parallelism to solve large computational applications often yields better speedups compared to either applying pure task parallelism or pure data parallelism. Typically, the applications are modeled in terms of a dependence graph of coarsegrain dataparallel tasks, called a dataparallel task graph. In this paper we present a new compiletime heuristic, named Critical Path Reduction (CPR), for scheduling dataparallel task graphs. Experimental results based on graphs derived from real problems as well as synthetic graphs, show that CPR achieves higher speedup compared to other wellknown existing scheduling algorithms, at the expense of some higher cost. These results are also confirmed by performance measurements of two real applications (i.e., complex matrix multiplication and Strassen matrix multiplication) running on a cluster of workstations.
Benchmarking optimization software with cops 3.0
 MATHEMATICS AND COMPUTER SCIENCE DIVISION, ARGONNE NATIONAL LABORATORY
, 2004
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Towards an Autonomous, Humanoid, and Dynamically Walking Robot: Modeling, OPTIMAL TRAJECTORY PLANNING, HARDWARE ARCHITECTURE, AND EXPERIMENTS
 PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON HUMANOID ROBOTS
, 2003
"... The development process to achieve walking motion with a recently constructed humanoid robot is discussed. The desired motion is based on the solution of an optimal control problem whose constraints depend upon the highdimensional nonlinear multibody system dynamics of the 17 DoF humanoid and phys ..."
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Cited by 15 (11 self)
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The development process to achieve walking motion with a recently constructed humanoid robot is discussed. The desired motion is based on the solution of an optimal control problem whose constraints depend upon the highdimensional nonlinear multibody system dynamics of the 17 DoF humanoid and physical contact constraints with the environment. Online control strategies are developed to track the precalculated trajectories. Experimental walking results with the humanoid robot are presented.
Optimality measures for performance profiles
 Preprint ANL/MCSP11550504, Mathematics and Computer Science Division, Argonne National Lab
, 2004
"... We examine the influence of optimality measures on the benchmarking process, and show that scaling requirements lead to a convergence test for nonlinearly constrained solvers that uses a mixture of absolute and relative error measures. We show that this convergence test is well behaved at any point ..."
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Cited by 15 (0 self)
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We examine the influence of optimality measures on the benchmarking process, and show that scaling requirements lead to a convergence test for nonlinearly constrained solvers that uses a mixture of absolute and relative error measures. We show that this convergence test is well behaved at any point where the constraints satisfy the MangasarianFromovitz constraint qualification and also avoids the explicit use of a complementarity measure. Our computational experiments explore the impact of this convergence test on the benchmarking process with performance profiles. 1
The role of motion dynamics in the design, control and stability of bipedal and quadrupedal robots
, 2002
"... Abstract. Fundamental principles and recent methods for investigating the nonlinear dynamics of legged robot motions with respect to control, stability and design are discussed. One of them is the still challenging problem of producing dynamically stable gaits. The generation of fast walking or runn ..."
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Cited by 13 (3 self)
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Abstract. Fundamental principles and recent methods for investigating the nonlinear dynamics of legged robot motions with respect to control, stability and design are discussed. One of them is the still challenging problem of producing dynamically stable gaits. The generation of fast walking or running motions require methods and algorithms adept at handling the nonlinear dynamical effects and stability issues which arise. Reduced, recursive multibody algorithms, a numerical optimal control package, and new stability and energy performance indices are presented which are wellsuited for this purpose. Difficulties and open problems are discussed along with numerical investigations into the proposed gait generation scheme. Our analysis considers both biped and quadrupedal gaits with particular reference to the problems arising in soccerplaying tasks encountered at the RoboCup where our team, the Darmstadt Dribbling Dackels, participates as part of the German Team in the Sony Legged Robot League.