Related papers: Implied Integrality in Mixed-Integer Optimization
The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general…
We study the problem of verifiable polynomial evaluation in the user-server and multi-party setups. We propose {INTERPOL}, an information-theoretically verifiable algorithm that allows a user to delegate the evaluation of a polynomial to a…
Missing data represents a fundamental challenge in machine learning applications, often reducing model performance and reliability. This problem is particularly acute in fields like bioinformatics and clinical machine learning, where…
A Reduction -- an accumulation over a set of values, using an associative and commutative operator -- is a common computation in many numerical computations, including scientific computations, machine learning, computer vision, and…
Integration is indispensable, not only in mathematics, but also in a wide range of other fields. A deep learning method has recently been developed and shown to be capable of integrating mathematical functions that could not previously be…
We introduce a family of implicit probabilistic integrators for initial value problems (IVPs), taking as a starting point the multistep Adams-Moulton method. The implicit construction allows for dynamic feedback from the forthcoming…
Sleep quality is influenced by a complex interplay of behavioral, environmental, and psychosocial factors, yet most computational studies focus mainly on predictive risk identification rather than actionable intervention design. Although…
We introduce an efficient combination of polyhedral analysis and predicate partitioning. Template polyhedral analysis abstracts numerical variables inside a program by one polyhedron per control location, with a priori fixed directions for…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems are generally solved approximately using variations on…
We present a method for identifying groups of test examples -- slices -- on which a model under-performs, a task now known as slice discovery. We formalize coherence -- a requirement that erroneous predictions, within a slice, should be…
We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic…
The ability to integrate information in the brain is considered to be an essential property for cognition and consciousness. Integrated Information Theory (IIT) hypothesizes that the amount of integrated information ($\Phi$) in the brain is…
Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel…
This paper introduces a novel physics-informed impact identification (Phy-ID) framework. The proposed method integrates observational, inductive, and learning biases to combine physical knowledge with data-driven inference in a unified…
We give an explicit geometric way to build mixed-integer programming (MIP) formulations for unions of polyhedra. The construction is simply described in terms of spanning hyperplanes in an r-dimensional linear space. The resulting MIP…
Mixed integer predictive control deals with optimizing integer and real control variables over a receding horizon. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
Submodularity is a key property in discrete optimization. Submodularity has been widely used for analyzing the greedy algorithm to give performance bounds and providing insight into the construction of valid inequalities for mixed-integer…