First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for constrained convex programs, for which the constraint set is represented by affine equations and smooth nonlinear inequalities. Both methods are based on the classic...

Safe reinforcement learning considers practical scenarios that maximize the return while satisfying safety constraints. Current algorithms, which suffer from training oscillations or approximation errors, still struggle to update policy efficiently with precise constraint satisfaction. In this article, we propose Augmented Proximal Policy Optimization (APPO), augments Lagrangian function of pri...

Clustering is one of the most fundamental and important tasks in data mining. Traditional clustering algorithms, such as K-means, assign every data point to exactly one cluster. However, in real-world datasets, the clusters may overlap with each other. Furthermore, often, there are outliers that should not belong to any cluster. We recently proposed the NEO-K-Means (Non-Exhaustive, Overlapping ...

This paper presents a framework that unifies various search mechanisms for solving constrained nonlinear programming (NLP) problems. These problems are characterized by functions that are not necessarily differentiable and continuous. Our proposed framework is based on the first-order necessary and sufficient condition for constrained local minimization in discrete space that shows the equivale...

Abstract. An observation-based method (OBM) is developed to investigate the sensitivity of ozone formation precursors during two persistent elevated episodes observed at 77 stations in Guangdong. Average OH concentrations derived between 08:00 and 13:00 local time stay within a narrow range 2.5×106 5.5×106 cm−3 with weak dependence on NOx. These values are good agreement rural station Pearl Riv...

We present local convergence analysis of the method of multipliers for equality-constrained variational problems (in the special case of optimization, also called the augmented Lagrangian method) under the sole assumption that the dual starting point is close to a noncritical Lagrange multiplier (which is weaker than second-order sufficiency). Local superlinear convergence is established under ...

Introductions are given to key technologies of various Mixed and Augmented Reality systems developed and realized at Beijing Institute of Technology. The automatic calibration method for the multi-projector systems is studied and a new constrained color-matching algorithm has been investigated to remove the color variations. The optical see-through head-mounted display (OST-HMD) utilizing an ul...

Distributed learning in expert referral networks is a new Active Learning paradigm where experts—humans or automated agents—solve problems if they can or refer said problems to others with more appropriate expertise. Recent work augmented the basic learning-to-refer method with proactive skill posting, where experts may report their top skills to their colleagues, and proposed a modified algori...

This paper presents a computationally efficient method for solving generalized network problems with an additional linear constraint. The method is basically the primal simplex method specialized to exploit the topological structure of the problem. The method is similar to the specialization of Charnes and Cooper's Double Reverse Method by Meier, and Klingman and Russell for constrained pure ne...

We discuss the question of which features and/or properties make a method for solving a given problem belong to the “Newtonian class.” Is it the strategy of linearization (or perhaps, second-order approximation) of the problem data (maybe only part of the problem data)? Or is it fast local convergence of the method under natural assumptions and at a reasonable computational cost of its iteratio...