We analyze a trust region version of Newton's method for bound-constrained problems. Our approach relies on the geometry of the feasible set, not on the particular representation in terms of constraints. The convergence theory holds for linearly-constrained problems, and yields global and superlinear convergence without assuming neither strict complementarity nor linear independence of the active constraints. We also show that the convergence theory leads to an efficient implementation for large bound-constrained problems.

With technology scaling, the trend for high performance integrated circuits is towards ever higher operating frequency, lower power supply voltages and higher power dissipation.

KINEMATIC CONTROL OF HUMAN POSTURES FOR TASK SIMULATION XINMIN ZHAO NORMAN I. BADLER Kinematic control of human postures for task simulation is important in human factor analysis, simulation and training. It is a challenge to control the postures of a synthesized human figure in real-time on today's graphics workstations because the human body is highly articulated. In addition, we need to consider many spatial restrictions imposed on the human body while performing a task. In this study, we simplify the human posture control problem by decoupling the degrees of freedom (dof) in the human body. Based on several decoupling schemes, we develop an analytical human posture control algorithm. This analytical algorithm has a number of advantages over existing methods. It eliminates the local minima problem, it is efficient enough to control whole human body postures in real-time, and it provides more effective and convenient control over redundant degrees of freedom. The limitation of this a...

Control of physical simulation has become a popular topic in the field of computer graphics. Keyframe control has been applied to simulations of rigid bodies, smoke, liquid, flocks, and finite element-based elastic bodies. In this paper, we create a framework for controlling systems of interacting particles – paying special attention to simulations of cloth and flocking behavior. We introduce a novel integrator-swapping approximation in order to apply the adjoint method to linearized implicit schemes appropriate for cloth simulation. This allows the control of cloth while avoiding computationally infeasible derivative calculations. Meanwhile, flocking control using the adjoint method is significantly more efficient than currently-used methods for constraining group behaviors, allowing the controlled simulation of greater numbers of agents in fewer optimization iterations. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Physically based modeling; I.3.7 [Computer Graphics]: Animation; I.6.8 [Simulation and Modeling]: Animation;

The Network-Enabled Optimization System (NEOS) is an environment for solving optimization problems over the Internet. Users submit optimization problems to the NEOS Server via e-mail, the World Wide Web, or the NEOS Submission Tool. The NEOS Server locates the appropriate optimization solver, computes all additional information (for example, derivatives and sparsity patterns) required by the solver, links the optimization problem with the solver, and returns a solution. This article discusses the design and implementation of the NEOS Server. 1 Introduction The Network-Enabled Optimization System (NEOS) is an Internet-based service for optimization. The goal of NEOS is to be the definitive site for optimization information and technology, providing users not only with up-to-date literature on optimization but ready access to a growing library of optimization software. The main components of NEOS are the NEOS Guide and the NEOS Server. The NEOS Guide is a Web-based guide to optimization...

We present a framework for designing fast and monotonic algorithms for transmission tomography penalizedlikelihood image reconstruction. The new algorithms are based on paraboloidal surrogate functions for the loglikelihood. Due to the form of the log-likelihood function, it is possible to find low curvature surrogate functions that guarantee monotonicity. Unlike previous methods, the proposed surrogate functions lead to monotonic algorithms even for the nonconvex log- likelihood that arises due to background events such as scatter and random coincidences. The gradient and the curvature of the likelihood terms are evaluated only once per iteration. Since the problem is simplified, the CPU time per iteration is less than that of current algorithms which directly minimize the objective, yet the convergence rate is comparable. The simplicity, monotonicity and speed of the new algorithms are quite attractive. The convergence rates of the algorithms are demonstrated using real PET transmission scans. 1

This paper reviews advances in Newton, quasi-Newton and conjugate gradient methods for large scale optimization. It also describes several packages developed during the last ten years, and illustrates their performance on some practical problems. Much attention is given to the concept of partial separabilitywhich is gaining importance with the arrival of automatic differentiation tools and of optimization software that fully exploits its properties.

Classical multidimensional scaling constructs a configuration of points... This paper describes the computational theory that provides a common foundation for these formulations.

Abstract — In recent years, learning models from data has become an increasingly interesting tool for robotics, as it allows straightforward and accurate model approximation. However, in most robot learning approaches, the model is learned from scratch disregarding all prior knowledge about the system. For many complex robot systems, available prior knowledge from advanced physics-based modeling techniques can entail valuable information for model learning that may result in faster learning speed, higher accuracy and better generalization. In this paper, we investigate how parametric physical models (e.g., obtained from rigid body dynamics) can be used to improve the learning performance, and, especially, how semiparametric regression methods can be applied in this context. We present two possible semiparametric regression approaches, where the knowledge of the physical model can either become part of the mean function or of the kernel in a nonparametric Gaussian process regression. We compare the learning performance of these methods first on sampled data and, subsequently, apply the obtained inverse dynamics models in tracking control on a real Barrett WAM. The results show that the semiparametric models learned with rigid body dynamics as prior outperform the standard rigid body dynamics models on real data while generalizing better for unknown parts of the state space. I.

. In this paper, an unconstrained convex programming dual approach for solving a class of linear semi--infinite programming problems is proposed. Both primal and dual convergence results are established under some basic assumptions. Numerical examples are also included to illustrate this approach. Key words. Semi-infinite programming, linear programming, convex programming, entropy optimization. AMS subject classifications. 90C05, 90C34, 49M35 1. Introduction. Many linear semi--infinite programming problems including the L1 and Chebychev approximation problems [14, 15] appear in the following "dual form": Program (D) Max b T w s.t. a(t) T w c(t); 8t 2 T; (1.1) where b; w 2 R m , T is a compact set in R n , a(t) T = (a 1 (t); : : : ; am (t)), and c(t) and a j (t); j = 1; : : : ; m; are continuous functions defined on T . A corresponding "primal form" linear semi--infinite programming problem can be represented as follows. Program (P ) Min Z T c(t)x(t)d(t) s.t. Z T ...