Adjoint-based predictor-corrector sequential convex programming for parametric nonlinear optimization

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that guarantees the tracking performance of the algorithm. Two variants of this algorithm are investigated. The first one can be used to solve nonlinear programming problems while the second variant is aimed to treat online parametric nonlinear programming problems. The local convergence of these variants is proved. An application to a large-scale benchmark problem that originates from nonlinear model predictive control of a hydro power plant is implemented to examine the performance of the algorithms.Comment: This manuscript consists of 25 pages and 7 figure

Probabilistic Models over Ordered Partitions with Application in Learning to Rank

This paper addresses the general problem of modelling and learning rank data with ties. We propose a probabilistic generative model, that models the process as permutations over partitions. This results in super-exponential combinatorial state space with unknown numbers of partitions and unknown ordering among them. We approach the problem from the discrete choice theory, where subsets are chosen in a stagewise manner, reducing the state space per each stage significantly. Further, we show that with suitable parameterisation, we can still learn the models in linear time. We evaluate the proposed models on the problem of learning to rank with the data from the recently held Yahoo! challenge, and demonstrate that the models are competitive against well-known rivals.Comment: 19 pages, 2 figure

Preference Networks: Probabilistic Models for Recommendation Systems

Recommender systems are important to help users select relevant and personalised information over massive amounts of data available. We propose an unified framework called Preference Network (PN) that jointly models various types of domain knowledge for the task of recommendation. The PN is a probabilistic model that systematically combines both content-based filtering and collaborative filtering into a single conditional Markov random field. Once estimated, it serves as a probabilistic database that supports various useful queries such as rating prediction and top-$N$ recommendation. To handle the challenging problem of learning large networks of users and items, we employ a simple but effective pseudo-likelihood with regularisation. Experiments on the movie rating data demonstrate the merits of the PN.Comment: In Proc. of 6th Australasian Data Mining Conference (AusDM), Gold Coast, Australia, pages 195--202, 200

Polyadic Constacyclic Codes

For any given positive integer $m$, a necessary and sufficient condition for the existence of Type I $m$-adic constacyclic codes is given. Further, for any given integer $s$, a necessary and sufficient condition for $s$ to be a multiplier of a Type I polyadic constacyclic code is given. As an application, some optimal codes from Type I polyadic constacyclic codes, including generalized Reed-Solomon codes and alternant MDS codes, are constructed.Comment: We provide complete solutions on two basic questions on polyadic constacyclic cdes, and construct some optimal codes from the polyadic constacyclic cde