Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM). The most computationally expensive procedure in IPMs is to solve systems of linear equations via matrix factorization. Recently, machine learning techniques have been adopted to expedite classic optimization algorithms. In this work, we propose using Long Short-Term Memory (LSTM) neural networks to approximate the solution of linear systems and integrate this approximating step into an IPM. The resulting approximate NLP solution is then utilized to warm-start an interior point solver. Experiments on various types of NLPs, including Quadratic Programs and Quadratically Constrained Quadratic Programs, show that our approach can significantly accelerate NLP solving, reducing iterations by up to 60% and solution time by up to 70% compared to the default solver.

Extensive applications of Zi-Yuan 3 (ZY-3) satellite imagery of China have commenced since its on-orbit test was finished. Most of the data are processed scene by scene with a few ground control points (GCPs) for each scene; this conventional method is mature and widely used all over the world. However, very little work has focused on its application to super large area blocks. This letter aims to study mapping applications without GCPs for a super large area, which is defined as a range of interprovincial or even nationwide areas. The automatic matching and bundle block adjustment (BBA) software developed by our research team are applied to deal with two blocks of ZY-3 three-line camera imagery which covers most of the provinces in eastern China. Our comparison analysis of different data processing methods and the geolocation accuracies of the overlapped areas between adjacent strips are presented in this letter, as well as the possibility of nationwide BBA. The preliminary test results show that multistrip BBA without GCPs can achieve accuracies of about 13-15 m in both planimetry and height, which means that nationwide BBA is considered practical and feasible.

ZY-3, which was launched on January 9, 2012, is the first stereo mapping satellite in China. The initial accuracy of direct georeferencing with the onboard three-line camera (TLC) imagery is low. Sensor geometric calibration with bundle block adjustment is used to improve the georeferencing accuracy. A new on-orbit sensor calibration method that can correct the misalignment angles between the spacecraft and the TLC and the misalignment of charge-coupled device is described. All of the calibration processes are performed using a multistrip data set. The control points are automatically matched from existing digital ortho map and digital elevation model. To fully evaluate the accuracy of different calibration methods, the calibrated parameters are used as input data to conduct georeferencing and bundle adjustment with a total of 19 strips of ZY-3 TLC data. A systematic error compensation model is introduced as the sensor model in bundle adjustment to compensate for the position and attitude errors. Numerous experiments demonstrate that the new calibration model can largely improve the external accuracy of direct georeferencing from the kilometer level to better than 20 m in both plane and height. A further bundle block adjustment with medium-accuracy ground control points (GCPs), using these calibrated parameters, can achieve external accuracy of about 4 m in plane and 3 m in height. Higher accuracy of about 1.3 m in plane and 1.7 m in height can be achieved by bundle adjustment using high-accuracy GCPs.