Smoothing Approximation to the Square-Root Exact Penalty Function

A second-order differentiable smoothing approximation lower order exact penalty function

In this paper, we give a smoothing approximation to the lower order exact penalty functions for inequality-constrained optimization problems. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem, of the nonsmooth penalty problem and of the original optimization problem. An algorithm based on the smoothed penalty function is presented, which ...

An Approximation for the Inverse Square Root Function

Fast Incremental Square Root Information Smoothing

We propose a novel approach to the problem of simultaneous localization and mapping (SLAM) based on incremental smoothing, that is suitable for real-time applications in large-scale environments. The main advantages over filter-based algorithms are that we solve the full SLAM problem without the need for any approximations, and that we do not suffer from linearization errors. We achieve efficie...

Square Root SAM: Simultaneous Localization and Mapping via Square Root Information Smoothing

Solving the SLAM problem is one way to enable a robot to explore, map, and navigate in a previously unknown environment. We investigate smoothing approaches as a viable alternative to extended Kalman filter-based solutions to the problem. In particular, we look at approaches that factorize either the associated information matrix or the measurement Jacobian into square root form. Such technique...

Square-root information filtering and fixed-interval smoothing with singularities

The square-root information filter and smoother algorithms have been generalized to handle singular state transition matrices and perfect measurements. This has been done to allow the use of SRIF techniques for problems with delays and state constraints. The generalized algorithms use complete QR factorization to isolate deterministically known parts of the state and nonsingular parts of the st...