On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization

There is a natural norm associated with a starting point of the homogeneous self-dual (HSD) embedding model for conic convex optimization. In this norm two measures of the HSD model’s behavior are precisely controlled independent of the problem instance: (i) the sizes of ε-optimal solutions, and (ii) the maximum distance of ε-optimal solutions to the boundary of the cone of the HSD variables. This norm is also useful in developing a stopping-rule theory for HSD-based interior-point methods such as SeDuMi. Under mild assumptions, we show that a standard stopping rule implicitly involves the sum of the sizes of the ε-optimal primal and dual solutions, as well as the size of the initial primal and dual infeasibility residuals. This theory suggests possible criteria for developing starting points for the homogeneous self-dual model that might improve the resulting solution time in practice

Proceedings of the Fourth PHANTOM Users Group Workshop

This Report contains the proceedings of the Fourth Phantom Users Group Workshop contains 17 papers presented October 9-12, 1999 at MIT Endicott House in Dedham Massachusetts. The workshop included sessions on, Tools for Programmers, Dynamic Environments, Perception and Cognition, Haptic Connections, Collision Detection / Collision Response, Medical and Seismic Applications, and Haptics Going Mainstream. The proceedings include papers that cover a variety of subjects in computer haptics including rendering, contact determination, development libraries, and applications in medicine, path planning, data interaction and training.

Proceedings of the Second PHANToM User's Group Workshop

On October 19-22, 1997 the Second PHANToM Users Group Workshop was held at the MIT Endicott House in Dedham, Massachusetts. Designed as a forum for sharing results and insights, the workshop was attended by more than 60 participants from 7 countries. These proceedings report on workshop presentations in diverse areas including rigid and compliant rendering, tool kits, development environments, techniques for scientific data visualization, multi-modal issues and a programming tutorial.

A Proposal for Enterprise Value Phase of the Lean Aerospace Initiative

The Massachusetts Institute of Technology (MIT) submits this proposal for the Enterprise Value Phase of the Lean Aerospace Initiative (LAI) in response to the October 9, 2002 Request for Proposal (RFP) F33615-02-2-5501 from the Air Force Research Laboratory (AFRL/MLKT), Wright-Patterson Air Force Base, Ohio. This proposal addresses the conduct of the LAI as set forth in the Enterprise Value Phase Concept of Operations (final draft dated 5 June 2002. The creation of this Enterprise Value Phase Concept of Operations (ConOps) was the result of extensive interaction among all stakeholders in the LAI consortium. The proposed products and research topics have been developed by the MIT LAI team based on this extended interaction with the Lean Aerospace Initiative consortium members during the concept of operations development. This proposal is in consonance with the Enterprise Value Phase vision, and mission as set forth in the concept of operations so as to meet stakeholder needs to achieve the goals and deliverables desired, prioritized to fit available funding.

Thermal Noise Behavior of the Bridge Circuit

This paper considers a connection between the deterministic and noisy behavior of nonlinear networks. Specifically, a particular bridge circuit is examined which has two possibly nonlinear energy storage elements. By proper choice of the constitutive relations for the network elements, the deterministic terminal behavior reduces to that of a single linear resistor. This reduction of the deterministic terminal behavior, in which a natural frequency of a linear circuit does not appear in the driving-point impedance, has been shown in classical circuit theory books (e.g. [1, 2]). The paper shows that, in addition to the reduction of the deterministic behavior, the thermal noise at the terminals of the network, arising from the usual Nyquist-Johnson noise model associated with each resistor in the network, is also exactly that of a single linear resistor. While this result for the linear time-invariant (LTI) case is a direct consequence of a well-known result for RLC circuits, the nonlinear result is novel. We show that the terminal noise current is precisely that predicted by the Nyquist-Johnson model for R if the driving voltage is zero or constant, but not if the driving voltage is time-dependent or the inductor and capacitor are time-varying