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A key problem in multiobjective linear programming is to find the set of all efficient extreme points in objective space. In this paper we introduce oriented projective geometry as an efficient and effective framework for solving this…
The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper, we provide the first algorithmic applications of tree-cut…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
The predict+optimize problem combines machine learning ofproblem coefficients with a combinatorial optimization prob-lem that uses the predicted coefficients. While this problemcan be solved in two separate stages, it is better to…
Network partitioning has gained recent attention as a pathway to enable decentralized operation and control in large-scale systems. This paper addresses the interplay between partitioning, observability, and sensor placement (SP) in dynamic…
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements.…
Convex maximization encompasses a broad class of optimization problems and is generally NP-hard, even for low-rank objectives. This paper investigates structural conditions under which convex maximization becomes polynomially solvable. From…
Neural PDE solvers used for scientific simulation often violate governing equation constraints. While linear constraints can be projected cheaply, many constraints are nonlinear, complicating projection onto the feasible set. Dynamical PDEs…
Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…
A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…
We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability,…
Linearizability has become the de facto correctness specification for implementations of concurrent data structures. While formally verifying such implementations remains challenging, linearizability monitoring has emerged as a promising…
In real-time systems optimization, designers often face a challenging problem posed by the non-convex and non-continuous schedulability conditions, which may even lack an analytical form to understand their properties. To tackle this…
Optimization under structural constraints is typically analyzed through projection or penalty methods, obscuring the geometric mechanism by which constraints shape admissible dynamics. We propose an operator-theoretic formulation in which…
There is a subset of computational problems that are computable in polynomial time for which an existing algorithm may not complete due to a lack of high performance technology on a mission field. We define a subclass of deterministic…
Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
Infinite-dimensional optimization (InfiniteOpt) problems involve modeling components (variables, objectives, and constraints) that are functions defined over infinite-dimensional domains. Examples include continuous-time dynamic…