11,407 research outputs found
Conic Optimization Theory: Convexification Techniques and Numerical Algorithms
Optimization is at the core of control theory and appears in several areas of
this field, such as optimal control, distributed control, system
identification, robust control, state estimation, model predictive control and
dynamic programming. The recent advances in various topics of modern
optimization have also been revamping the area of machine learning. Motivated
by the crucial role of optimization theory in the design, analysis, control and
operation of real-world systems, this tutorial paper offers a detailed overview
of some major advances in this area, namely conic optimization and its emerging
applications. First, we discuss the importance of conic optimization in
different areas. Then, we explain seminal results on the design of hierarchies
of convex relaxations for a wide range of nonconvex problems. Finally, we study
different numerical algorithms for large-scale conic optimization problems.Comment: 18 page
Adapting the interior point method for the solution of linear programs on high performance computers
In this paper we describe a unified algorithmic framework for the interior point method (IPM) of solving Linear Programs (LPs) which allows us to adapt it over a range of high performance computer architectures. We set out the reasons as to why IPM makes better use of high performance computer architecture than the sparse simplex method. In the inner iteration of the IPM a search direction is computed using Newton or higher order methods. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system and the design of data structures to take advantage of coarse grain parallel and massively parallel computer architectures are considered in detail. Finally, we present experimental results of solving NETLIB test problems on examples of these architectures and put forward arguments as to why integration of the system within sparse simplex is beneficial
Exponential Integrators on Graphic Processing Units
In this paper we revisit stencil methods on GPUs in the context of
exponential integrators. We further discuss boundary conditions, in the same
context, and show that simple boundary conditions (for example, homogeneous
Dirichlet or homogeneous Neumann boundary conditions) do not affect the
performance if implemented directly into the CUDA kernel. In addition, we show
that stencil methods with position-dependent coefficients can be implemented
efficiently as well.
As an application, we discuss the implementation of exponential integrators
for different classes of problems in a single and multi GPU setup (up to 4
GPUs). We further show that for stencil based methods such parallelization can
be done very efficiently, while for some unstructured matrices the
parallelization to multiple GPUs is severely limited by the throughput of the
PCIe bus.Comment: To appear in: Proceedings of the 2013 International Conference on
High Performance Computing Simulation (HPCS 2013), IEEE (2013
Imposing Economic Constraints in Nonparametric Regression: Survey, Implementation and Extension
Economic conditions such as convexity, homogeneity, homotheticity, and monotonicity are all important assumptions or consequences of assumptions of economic functionals to be estimated. Recent research has seen a renewed interest in imposing constraints in nonparametric regression. We survey the available methods in the literature, discuss the challenges that present themselves when empirically implementing these methods and extend an existing method to handle general nonlinear constraints. A heuristic discussion on the empirical implementation for methods that use sequential quadratic programming is provided for the reader and simulated and empirical evidence on the distinction between constrained and unconstrained nonparametric regression surfaces is covered.identification, concavity, Hessian, constraint weighted bootstrapping, earnings function
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