949 research outputs found
An unexpected application of minimization theory to module decompositions
The aim of this work is to show how we can decompose a module (if
decomposable) into an indecomposable module with the help of the minimization
process.Comment: 15-02-200
Relative Entropy Relaxations for Signomial Optimization
Signomial programs (SPs) are optimization problems specified in terms of
signomials, which are weighted sums of exponentials composed with linear
functionals of a decision variable. SPs are non-convex optimization problems in
general, and families of NP-hard problems can be reduced to SPs. In this paper
we describe a hierarchy of convex relaxations to obtain successively tighter
lower bounds of the optimal value of SPs. This sequence of lower bounds is
computed by solving increasingly larger-sized relative entropy optimization
problems, which are convex programs specified in terms of linear and relative
entropy functions. Our approach relies crucially on the observation that the
relative entropy function -- by virtue of its joint convexity with respect to
both arguments -- provides a convex parametrization of certain sets of globally
nonnegative signomials with efficiently computable nonnegativity certificates
via the arithmetic-geometric-mean inequality. By appealing to representation
theorems from real algebraic geometry, we show that our sequences of lower
bounds converge to the global optima for broad classes of SPs. Finally, we also
demonstrate the effectiveness of our methods via numerical experiments
Repairing triangle meshes built from scanned point cloud
The Reverse Engineering process consists of a succession of operations that aim at creating a digital representation of a physical model. The reconstructed geometric model is often a triangle mesh built from a point cloud acquired with a scanner. Depending on both the object complexity and the scanning process, some areas of the object outer surface may never be accessible, thus inducing some deficiencies in the point cloud and, as a consequence, some holes in the resulting mesh. This is simply not acceptable in an integrated design process where the geometric models are often shared between the various applications (e.g. design, simulation, manufacturing). In this paper, we propose a complete toolbox to fill in these undesirable holes. The hole contour is first cleaned to remove badly-shaped triangles that are due to the scanner noise. A topological grid is then inserted and deformed to satisfy blending conditions with the surrounding mesh. In our approach, the shape of the inserted mesh results from the minimization of a quadratic function based on a linear mechanical model that is used to approximate the curvature variation between the inner and surrounding meshes. Additional geometric constraints can also be specified to further shape the inserted mesh. The proposed approach is illustrated with some examples coming from our prototype software
Relative Entropy Relaxations for Signomial Optimization
Signomial programs (SPs) are optimization problems specified in terms of signomials,
which are weighted sums of exponentials composed with linear functionals of a decision variable. SPs
are nonconvex optimization problems in general, and families of NP-hard problems can be reduced
to SPs. In this paper we describe a hierarchy of convex relaxations to obtain successively tighter
lower bounds of the optimal value of SPs. This sequence of lower bounds is computed by solving
increasingly larger-sized relative entropy optimization problems, which are convex programs specified
in terms of linear and relative entropy functions. Our approach relies crucially on the observation
that the relative entropy function, by virtue of its joint convexity with respect to both arguments,
provides a convex parametrization of certain sets of globally nonnegative signomials with efficiently
computable nonnegativity certificates via the arithmetic-geometric-mean inequality. By appealing to
representation theorems from real algebraic geometry, we show that our sequences of lower bounds
converge to the global optima for broad classes of SPs. Finally, we also demonstrate the effectiveness
of our methods via numerical experiments
NASA space station automation: AI-based technology review
Research and Development projects in automation for the Space Station are discussed. Artificial Intelligence (AI) based automation technologies are planned to enhance crew safety through reduced need for EVA, increase crew productivity through the reduction of routine operations, increase space station autonomy, and augment space station capability through the use of teleoperation and robotics. AI technology will also be developed for the servicing of satellites at the Space Station, system monitoring and diagnosis, space manufacturing, and the assembly of large space structures
Repairing triangle meshes built from scanned point cloud
International audienceThe Reverse Engineering process consists of a succession of operations that aim at creating a digital representation of a physical model. The reconstructed geometric model is often a triangle mesh built from a point cloud acquired with a scanner. Depending on both the object complexity and the scanning process, some areas of the object outer surface may never be accessible, thus inducing some deficiencies in the point cloud and, as a consequence, some holes in the resulting mesh. This is simply not acceptable in an integrated design process where the geometric models are often shared between the various applications (e.g. design, simulation, manufacturing). In this paper, we propose a complete toolbox to fill in these undesirable holes. The hole contour is first cleaned to remove badly-shaped triangles that are due to the scanner noise. A topological grid is then inserted and deformed to satisfy blending conditions with the surrounding mesh. In our approach, the shape of the inserted mesh results from the minimization of a quadratic function based on a linear mechanical model that is used to approximate the curvature variation between the inner and surrounding meshes. Additional geometric constraints can also be specified to further shape the inserted mesh. The proposed approach is illustrated with some examples coming from our prototype software
Repairing triangle meshes built from scanned point cloud
International audienceThe Reverse Engineering process consists of a succession of operations that aim at creating a digital representation of a physical model. The reconstructed geometric model is often a triangle mesh built from a point cloud acquired with a scanner. Depending on both the object complexity and the scanning process, some areas of the object outer surface may never be accessible, thus inducing some deficiencies in the point cloud and, as a consequence, some holes in the resulting mesh. This is simply not acceptable in an integrated design process where the geometric models are often shared between the various applications (e.g. design, simulation, manufacturing). In this paper, we propose a complete toolbox to fill in these undesirable holes. The hole contour is first cleaned to remove badly-shaped triangles that are due to the scanner noise. A topological grid is then inserted and deformed to satisfy blending conditions with the surrounding mesh. In our approach, the shape of the inserted mesh results from the minimization of a quadratic function based on a linear mechanical model that is used to approximate the curvature variation between the inner and surrounding meshes. Additional geometric constraints can also be specified to further shape the inserted mesh. The proposed approach is illustrated with some examples coming from our prototype software
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