Abstract: Conditional Gradients (aka Frank-Wolfe Methods) are an important class of algorithms for smooth constraint convex minimization, in particular when projection onto the feasible region is non-trivial or sparse representation of iterates via extreme points is desired. Due to their simplicity, conditional gradient methods have become the methods of choice for many applications despite often suboptimal theoretical convergence rates. In fact, often the empirically observed rates are significantly better than the worst-case rates and recent refinements of the basic conditional gradients methods achieve, e.g., linear convergence in the strongly convex case or allow for variance-reduced stochastic variants. In this talk I will discuss some of these recent developments and discuss further extensions as well as open problems.

Abstract: Healthcare is clearly experiencing a data revolution. With advances in digital health records, genomic sequencing, continuing growth of social networks and media for community-health, and the emerging "App" market for health-related mobile and web-enabled applications – there is tremendous access and availability of private and public data for advancing precision medicine and improving population health. This ability to leverage these datasets for translational value, across the continuum of basic, preclinical, and clinical science will be critical for addressing in an effective and timely manner emerging personalized and population healthcare challenges. At the same time, artificial intelligence (AI) is making continuing advances in biomedicine. However, there are outstanding questions of how AI can provide actionable clinical insights. We will highlight promising health informatics applications while emphasizing the current and emerging challenges of ensuring their translational value and broad population impact.

Abstract: The core of the electricity market clearing software is large scale security constrained unit commitment and security constrained economic dispatch problems. Through the development of advanced modeling and the application of state of the art optimization solvers, the market clearing applications enabled Regional Transmission Operators to bring billions of dollars of benefit to the society. The power industry evolution has posed unprecedented challenges to the existing optimization and computation techniques. The drivers for these new challenges include the footprint expansion of electricity markets, the modeling requirements for more complicated resources such as fast-growing distributed energy resources (DER), virtual power plants (VPP), renewables and the necessity to manage increased uncertainty in market operations. This talk first shared the research and development led to the past success and the on-going efforts in developing new modeling and solution approaches to prepare for future challenges.

MIP practitioners solve large-scale mixed integer optimization problems to optimality or near-optimality by competent modelization and running a black-box branch-and-cut solver. This technology was enabled to a large part by the revival of Gomory's classic general-purpose cutting planes. Challenging new applications and increased data sizes now require the development of next-generation cutting-plane systems. In my talk I will give a brief review of cutgeneratingfunctionology, a framework for analyzing general-purpose cuts, and highlight some research challenges in this framework. I will then introduce computational methods, including automated proof techniques, that address these difficulties.