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Optimization networks are a new methodology for holistically solving interrelated problems that have been developed with combinatorial optimization problems in mind. In this contribution we revisit the core principles of optimization…
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in…
We present a novel adaptive optimization algorithm for black-box multi-objective optimization problems with binary constraints on the foundation of Bayes optimization. Our method is based on probabilistic regression and classification…
The distribution network restoration problem is by nature a mixed integer and non-linear optimization problem due to the switching decisions and Optimal Power Flow (OPF) constraints, respectively. The link between these two parts involves…
While looking for abductive explanations of a given set of manifestations, an ordering between possible solutions is often assumed. The complexity of finding/verifying optimal solutions is already known. In this paper we consider the…
Image foreground extraction is a classical problem in image processing and vision, with a large range of applications. In this dissertation, we focus on the extraction of text and graphics in mixed-content images, and design novel…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
A major limitation of exact inference algorithms for probabilistic graphical models is their extensive memory usage, which often puts real-world problems out of their reach. In this paper we show how we can extend inference algorithms,…
Optimally operating an integrated electricity-gas system (IEGS) is significant for the energy sector. However, the IEGS operation model's nonconvexity makes it challenging to solve the optimal dispatch problem in the IEGS. This letter…
We consider the worst-case load-shedding problem in electric power networks where a number of transmission lines are to be taken out of service. The objective is to identify a pre-specified number of line outage that leads to the maximum…
This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…
Although a large number of optimization algorithms have been proposed for black box optimization problems, the no free lunch theorems inform us that no algorithm can beat others on all types of problems. Different types of optimization…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
In our previous work [Singler, SIAM J. Numer. Anal. 52 (2014), no. 2, 852-876], we considered the proper orthogonal decomposition (POD) of time varying PDE solution data taking values in two different Hilbert spaces. We considered various…
We study the problem of learning similarity by using nonlinear embedding models (e.g., neural networks) from all possible pairs. This problem is well-known for its difficulty of training with the extreme number of pairs. For the special…
The encoding of solutions in black-box optimization is a delicate, handcrafted balance between expressiveness and domain knowledge -- between exploring a wide variety of solutions, and ensuring that those solutions are useful. Our main…
The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism…
The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way…
We develop a cutting-plane methodology that adjusts solutions to optimization problems so as to reduce features that bring about exposure to risk, such as concentration of assets or resources. The methodology is agnostic to the…