Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications, vari- able selection, and high-dimensional analysis. We propose a broad framework for sparse relaxed regularized regression, called SR3. The key idea is to solve a relaxation of … Read more
We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying that an image classification network is robust to adversarial inputs, or solving decision problems where the objective function is a machine learning model. … Read more
In this note, some results are introduced considering the assumptions of quasiconvexity and nonmonotonicity, finally an application and an idea to solve the quasiconvex equilibrium problem are presented considering these new results. ArticleDownload View PDF
We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i.e.\ problems where the cost of evaluating/enforcing of the (possibly nonconvex or even disconnected) constraints, if any, is negligible compared to that of evaluating the objective function. These bounds unify, extend or improve all known upper and lower complexity bounds … Read more
Many real-world decision-making problems can be modeled as network design problems, especially on networks with capacity requirements on links. In network design problems, decisions are made on installation of flow transfer capacities on the links and routing of flow from a set of source nodes to a set of sink nodes through the links. Many … Read more
High penetration of distributed energy resources (DERs) is transforming the paradigm in power system operation. The ability to provide electricity to customers while the main grid is disrupted has introduced the concept of microgrids with many challenges and opportunities. Emergency control of dangerous transients caused by the transition between the grid-connected and island modes in … Read more
Generator maintenance scheduling plays a pivotal role in ensuring uncompromising operations of power systems. There exists a tight coupling between the condition of the generators and corresponding operational schedules, significantly affecting reliability of the system. In this study, we effectively model and solve an integrated condition-based maintenance and operations scheduling problem for a fleet of … Read more
The purpose of this study is to give an exact formulation of optimization of volumetric-modulated arc therapy (VMAT) with sliding-window delivery, and to investigate the plan quality effects of decreasing the number of sliding-window sweeps made on the 360-degree arc for a faster VMAT treatment. In light of the exact formulation, we interpret an algorithm … Read more
Deep learning has recently attracted a significant amount of attention due to its great empirical success. However, the effectiveness in training deep neural networks (DNNs) remains a mystery in the associated nonconvex optimizations. In this paper, we aim to provide some theoretical understanding on such optimization problems. In particular, the Kurdyka-{\L}ojasiewicz (KL) property is established … Read more
Logistic regression is one of the most popular methods in binary classification, wherein estimation of model parameters is carried out by solving the maximum likelihood (ML) optimization problem, and the ML estimator is defined to be the optimal solution of this problem. It is well known that the ML estimator exists when the data is … Read more