Related papers: On the Complexity of Inverse Mixed Integer Linear …
Floor planning is an important and difficult task in architecture. When planning office buildings, rooms that belong to the same organisational unit should be placed close to each other. This leads to the following NP-hard mathematical…
The maximum graph bisection problem is a well known graph partition problem. The problem has been proven to be NP-hard. In the maximum graph bisection problem it is required that the set of vertices is divided into two partition with equal…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
This paper presents a new hybrid classical-quantum approach to solve Mixed Integer Linear Programming (MILP) using neutral atom quantum computations. We apply Benders decomposition (BD) to segment MILPs into a master problem (MP) and a…
We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
In this paper, we propose a new mixed-integer linear programming (MILP) model ontology and a novel constraint typology of MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life…
The Bayesian approach has proved to be a coherent approach to handle ill posed Inverse problems. However, the Bayesian calculations need either an optimization or an integral calculation. The maximum a posteriori (MAP) estimation requires…
In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed Integer Optimization (MIO) problems. We…
Inverse optimization describes a process that is the "reverse" of traditional mathematical optimization. Unlike traditional optimization, which seeks to compute optimal decisions given an objective and constraints, inverse optimization…
This paper revisits the modal truncation from an optimisation point of view. In particular, the concept of dominant poles is formulated with respect to different systems norms as the solution of the associated optimal modal truncation…
This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…
We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
Minimum distance constraints (minDCs) appear in many geometric optimization problems. They pose major challenges for mixed-integer nonlinear programming (MINLP) due to their reverse-convexity. We develop new algorithms for tightening…
Although knowing the feeder topology and line impedances is a prerequisite for solving any grid optimization task, utilities oftentimes have limited or outdated information on their electric network assets. Given the rampant integration of…
Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations.…
Lagrangian relaxation stands among the most efficient approaches for solving a Mixed Integer Linear Programs (MILP) with difficult constraints. Given any duals for these constraints, called Lagrangian Multipliers (LMs), it returns a bound…
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…
We describe a method to discretize optimization problems arising in the regularization of linear inverse problem having compact forward operator defined on 3-D valed measures, compactly supported on a fixed set. The criterion is a quadratic…
Influence diagrams represent decision-making problems with interdependencies between random events, decisions, and consequences. Traditionally, they have been solved using algorithms that determine the expected utility-maximizing decision…