Given recent deep learning results that demonstrate the ability to effectively optimize high-dimensional non-convex functions with gradient descent optimization on GPUs, we ask in this paper whether symbolic gradient optimization tools such as Tensorflow can be effective for planning in hybrid (mixed discrete and continuous) nonlinear domainswith high dimensional state and action spaces? To thi...

We present an improved microfluidic design for generating spatial and temporal gradients. The basic functional elements are bifurcated and trifurcated channels used to split flow between two and three channels, respectively. We use bifurcated channels on the exterior of the channel manifold and trifurcated channels in the interior with mixing tees to recombine flows. For N gradient-forming leve...

BOUND-CONSTRAINED MINIMIZATION PROBLEMS MARY ANN BRANCH , THOMAS F. COLEMAN AND YUYING LI Abstract. A subspace adaptation of the Coleman-Li trust region and interior method is proposed for solving large-scale bound-constrained minimization problems. This method can be implemented with either sparse Cholesky factorization or conjugate gradient computation. Under reasonable conditions the converg...

-----------------------------The efficient combination of directions is a significant problem in line search methods that either use negative curvature. or wish to include additional information such as the gradient or different approximations to the Newton direction. In thls paper we describe a new procedure to combine several of these directions within an interior-point primal-dual algorithm....

In this paper we present the continuous and discontinuous Galerkin methods in a unified setting for the numerical approximation of the transport dominated advection-reaction equation. Both methods are stabilized by the interior penalty method, more precisely by the jump of the gradient in the continuous case whereas in the discontinuous case the stabilization of the jump of the solution and opt...

Source based heterogeneous modelling is a powerful way of defining gradient materials within a volume. The current solutions do not take into account the topology of the object and can provide counter intuitive results for complex objects. This paper presents a method to interpolate material properties and attributes based on the accessibility of the points in respect to the material features d...

We consider a primal-dual short-step interior-point method for conic convex optimization problems for which exact evaluation of the gradient and Hessian of the primal and dual barrier functions is either impossible or prohibitively expensive. As our main contribution, we show that if approximate gradients and Hessians of the primal barrier function can be computed, and the relative errors in su...

A Projected-Gradient Underdetermined Newton-like algorithm will be introduced for finding a solution of a Horizontal Nonlinear Complementarity Problem (HNCP) corresponding to a feasible solution of a Mathematical Programming Problem with Complementarity Constraints (MPCC). The algorithm employs a combination of Interior-Point Newton-like and Projected-Gradient directions with a line-search proc...

A ray-theoretic account of the passage of light through a radially inhomogeneous transparent sphere has been used to establish the existence of multiple primary rainbows for some refractive index profiles. The existence of such additional bows is a consequence of a sufficiently attractive potential in the interior of the drop, i.e. the refractive index gradient should be sufficiently negative t...

Rewarding properties of psychostimulants result from reduced uptake and/or increased release of dopamine at mesolimbic synapses. As exemplified by cocaine, many psychostimulants act by binding to the dopamine uptake transporter. However, this does not explain the action of other psychostimulants, including amphetamine. As most psychostimulants are weak bases and dopamine uptake into synaptic ve...