arXiv subjects

Jize Zhang

Publications and source records attributed to Jize Zhang.

22 records · Page 2Linked to original sources

arXiv2019

Offline state estimation for hybrid systems via nonsmooth variable projection

A hybrid dynamical system switches between dynamic regimes at time- or state-triggered events. We propose an offline algorithm that simultaneously estimates discrete and continuous components of a hybrid system's state. We formulate state estimation as a continuous optimization problem by relaxing the discrete component and use a robust loss function to accommodate large changes in the continuous component during switching events. Subsequently, we develop a novel nonsmooth variable projection algorithm with Gauss-Newton updates to solve the state estimation problem and prove the algorithm's global convergence to stationary points. We demonstrate the effectiveness of our approach on simple piecewise-linear and -nonlinear mechanical systems undergoing intermittent impact.

math.OC↗

arXiv2018

Bounded Regression with Gaussian Process Projection

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian process is first imposed on the regression function whose posterior distribution is then projected onto the bounded space. The resulting projected measure is then used for inference. The projected sample path has closed form which facilitates efficient computations. In particular, our projection approach maintains a comparable computational efficiency with that of the original GP. The proposed method yield predictions that respects bound constraints everywhere, while allows varying bounds across the input domain. An extensive simulation study is carried out which demonstrates that the performance of our approach dominates that of the competitors. An application to real data set is also considered.

stat.ME↗

arXiv2018

A Relaxed Optimization Approach for Cardinality-Constrained Portfolio Optimization

A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client preferences as they seek to maximize return and limit risk. We develop a new approach to solve cardinality-constrained portfolio optimization problems, extending both Markowitz and conditional value at risk (CVaR) optimization models with cardinality constraints. We derive a continuous relaxation method for the NP-hard objective, which allows for very efficient algorithms with standard convergence guarantees for nonconvex problems. For smaller cases, where brute force search is feasible to compute the globally optimal cardinality- constrained portfolio, the new approach finds the best portfolio for the cardinality-constrained Markowitz model and a very good local minimum for the cardinality-constrained CVaR model. For higher dimensions, where brute-force search is prohibitively expensive, we find feasible portfolios that are nearly as efficient as their non-cardinality constrained counterparts.

math.OC↗

arXiv2018

Mean Reverting Portfolios via Penalized OU-Likelihood Estimation

We study an optimization-based approach to con- struct a mean-reverting portfolio of assets. Our objectives are threefold: (1) design a portfolio that is well-represented by an Ornstein-Uhlenbeck process with parameters estimated by maximum likelihood, (2) select portfolios with desirable characteristics of high mean reversion and low variance, and (3) select a parsimonious portfolio, i.e. find a small subset of a larger universe of assets that can be used for long and short positions. We present the full problem formulation, a specialized algorithm that exploits partial minimization, and numerical examples using both simulated and empirical price data.

q-fin.PM↗