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Inverse Kinematics Positioning Using Nonlinear Programming for Highly Articulated Figures
 ACM Transactions on Graphics
, 1994
"... An articulated figure is often modeled as a set of rigid segments connected with joints. Its configuration can be altered by varying the joint angles. Although it is straightforward to compute figure configurations given joint angles (forward kinematics), it is not so to find the joint angles for ..."
Abstract

Cited by 101 (9 self)
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An articulated figure is often modeled as a set of rigid segments connected with joints. Its configuration can be altered by varying the joint angles. Although it is straightforward to compute figure configurations given joint angles (forward kinematics), it is not so to find the joint angles for a desired configuration (inverse kinematics). Since the inverse kinematics problem is of special importance to an animator wishing to set a figure to a posture satisfying a set of positioning constraints, researchers have proposed many approaches. But when we try to follow these approaches in an interactive animation system where the object to operate on is as highly articulated as a realistic human figure, they fail in either generality or performance, and so a new approach is fostered. Our approach is based on nonlinear programming techniques. It has been used for several years in the spatial constraint system in the Jack TM human figure simulation software developed at the Compute...
LARGESCALE LINEARLY CONSTRAINED OPTIMIZATION
, 1978
"... An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is descr ..."
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Cited by 75 (11 self)
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An algorithm for solving largescale nonlinear ' programs with linear constraints is presented. The method combines efficient sparsematrix techniques as in the revised simplex method with stable quasiNewton methods for handling the nonlinearities. A generalpurpose production code (MINOS) is described, along with computational experience on a wide variety of problems.
Computing Limit Loads by Minimizing a Sum of Norms
, 1994
"... Abstract. This paper treats the problem of computing the collapse state in limit analysis for a solid with a quadratic yield condition, such as, for example, the von Mises condition. After discretization with the finite element method, using divergencefree elements for the plastic flow, the kinemat ..."
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Cited by 14 (3 self)
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Abstract. This paper treats the problem of computing the collapse state in limit analysis for a solid with a quadratic yield condition, such as, for example, the von Mises condition. After discretization with the finite element method, using divergencefree elements for the plastic flow, the kinematic formulation reduces to the problem of minimizing a sum of Euclidean vector norms, subject to a single linear constraint. This is a nonsmooth minimization problem, since many of the norms in the sum may vanish at the optimal point. Recently an efficient solution algorithm has been developed for this particular convex optimization problem in large sparse form. The approach is applied to test problems in limit analysis in two different plane models: plane strain and plates. In the first case more than 80 % of the terms in the objective function are zero in the optimal solution, causing extreme ill conditioning. In the second case all terms are nonzero. In both cases the method works very well, and problems are solved which are larger by at least an order of magnitude than previously reported. The relative accuracy for the solution of the discrete problems, measured by duality gap and feasibility, is typically of the order 10−8.
Newton methods for largescale linear inequalityconstrained minimization
 SIAM Journal on Optimization
, 1997
"... Abstract. Newton methods of the linesearch type for largescale minimization subject to linear inequality constraints are discussed. The purpose of the paper is twofold: (i) to give an active–settype method with the ability to delete multiple constraints simultaneously and (ii) to give a relatively ..."
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Cited by 7 (0 self)
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Abstract. Newton methods of the linesearch type for largescale minimization subject to linear inequality constraints are discussed. The purpose of the paper is twofold: (i) to give an active–settype method with the ability to delete multiple constraints simultaneously and (ii) to give a relatively short general convergence proof for such a method. It is also discussed how multiple constraints can be added simultaneously. The approach is an extension of a previous work by the same authors for equalityconstrained problems. It is shown how the search directions can be computed without the need to compute the reduced Hessian of the objective function. The convergence analysis states that every limit point of a sequence of iterates satisfies the secondorder necessary optimality conditions. Key words. linear inequalityconstrained minimization, negative curvature, modified Newton method, symmetric indefinite factorization, largescale minimization, linesearch method
AgentFacilitated RealTime Flexible Supply Chain Structuring
 In Proceedings of the 1999 Autonomous Agents Workshop on Agent Based Decision Support for Managing the Internet Enabled Supply Chain
, 1999
"... Electronic commerce and the vast amounts of realtime information available through means of EDI and the Internet are reshaping the way enterprises conduct business. A new computational infrastructure and models are needed for a business to gain a competitive edge through effective use of this infor ..."
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Cited by 5 (0 self)
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Electronic commerce and the vast amounts of realtime information available through means of EDI and the Internet are reshaping the way enterprises conduct business. A new computational infrastructure and models are needed for a business to gain a competitive edge through effective use of this information base. In this paper, we develop a model of interorganizational electronic commerce that explores various new choices and opportunities that the electronic marketplace offers. We explicitly address two major performance measures of supply chains  time and cost  in a unified fashion. In our work, we model different business entities as autonomous software agents interconnected via the Internet. The main research focus of our efforts is how to coordinate software agents in supply chains dynamically and flexibly such that goods and services can be delivered at the right time in a costeffective manner.
Computing Limit Loads By Minimizing a Sum of Norms
 IFIP
, 1994
"... This paper treats the problem of computing the collapse state in limit analysis for a solid with a quadratic yield condition, such as, for example, the Mises condition. After discretization with the finite element method, using divergencefree elements for the plastic flow, the kinematic formulation ..."
Abstract
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This paper treats the problem of computing the collapse state in limit analysis for a solid with a quadratic yield condition, such as, for example, the Mises condition. After discretization with the finite element method, using divergencefree elements for the plastic flow, the kinematic formulation turns into the problem of minimizing a sum of Euclidean vector norms, subject to a single linear constraint. This is a nonsmooth minimization problem, since many of the norms in the sum may vanish at the optimal point. However, efficient solution algorithms for this particular convex optimization problem have recently been developed. The method is applied to test problems in limit analysis in two different plane models: plane strain and plates. In the first case more than 80 percent of the terms in the sum are zero in the optimal solution, causing severe illconditioning. In the last case all terms are nonzero. In both cases the algorithm works very well, and problems are solved which are l...
ANIMATION OF HUMAN MOTION WITH INVERSE KINEMATICS USING NONLINEAR PROGRAMMING
, 2001
"... that I have read this thesis and that in my opinion it is fully adequate, ..."
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that I have read this thesis and that in my opinion it is fully adequate,
NorthHolland Publishing Company MATRIX FACTOR1ZATIONS IN OPTIMIZATION OF NON LINEAR FUNCTIONS SUBJECT TO LINEAR CONSTRAINTS*
, 1974
"... Several ways of implementing methods for solving nonlinear optimization problems involving linear inequality and equality constraints using numerically stable matrix factorizations are described. The methods considered all follow an active constraint set approach and include quadratic programming, v ..."
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Several ways of implementing methods for solving nonlinear optimization problems involving linear inequality and equality constraints using numerically stable matrix factorizations are described. The methods considered all follow an active constraint set approach and include quadratic programming, variable metric, and modified Newton methods. 1.
Engineering Laboratory. Real Time Inverse Kinematics with Joint Limits and Spatial Constraints
, 1989
"... A configuration of an articulated figure of joints and segments can sometimes be specified as spatial constraints. Constrained parts on the articulated figure are abstracted as end effectors, and the counterparts in the space are abstracted as goals. The goal (constraint) can be as simple as a posit ..."
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A configuration of an articulated figure of joints and segments can sometimes be specified as spatial constraints. Constrained parts on the articulated figure are abstracted as end effectors, and the counterparts in the space are abstracted as goals. The goal (constraint) can be as simple as a position, an orientation, a weighted combination of position and orientation, a line, a plane, a direction, and so on, or it could be as complicated as a region in the space. An articulated figure consists of various segments connected together by joints. Each joint has some degrees of freedom which are subject to joint limits and manual adjustment. This paper presents an efficient algorithm to adjust the joint angles subject to joint limits so that the set of end effectors concurrently attempt to achieve their respective goals. Users specify end effectors and goals: the program computes a final configuration in real time in the sense that actions appear to take no longer than actual physical activities would. If it is impossible to satisfy all the goals owing to the actual constraints, the program should end up with the best possibility according to the