Related papers: Optimality, identifiability, and sensitivity
A frequentist definition of sensitivity of a search for new phenomena is discussed, that has several useful properties. It is based on completely standard concepts, is generally applicable, and has a very clear interpretation. It is…
Identifying active constraints from a point near an optimal solution is important both theoretically and practically in constrained continuous optimization, as it can help identify optimal Lagrange multipliers and essentially reduces an…
The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…
Optimization - minimization or maximization - in the lattice of subsets is a frequent operation in Artificial Intelligence tasks. Examples are subset-minimal model-based diagnosis, nonmonotonic reasoning by means of circumscription, or…
We study the fundamental question of how informative a dataset is for solving a given decision-making task. In our setting, the dataset provides partial information about unknown parameters that influence task outcomes. Focusing on linear…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
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 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,…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
Reliable predictions from systems biology models require knowing whether parameters can be estimated from available data, and with what certainty. Identifiability analysis reveals whether parameters are learnable in principle (structural…
We consider linear optimization over a fixed compact convex feasible region that is semi-algebraic (or, more generally, "tame"). Generically, we prove that the optimal solution is unique and lies on a unique manifold, around which the…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
Optimal solutions of combinatorial optimization problems can be sensitive to changes in the cost of one or more elements of the ground set E. Single and set tolerances measure the supremum / infimum possible change such that the current…
We derive asymptotically optimal statistical decision rules for discrete choice problems when payoffs depend on a partially-identified parameter $\theta$ and the decision maker can use a point-identified parameter $\mu$ to deduce…
We study the problem of determining what data is required to solve a decision-making task when only partial information about the state of the world is available. Focusing on linear programs, we introduce a decision-focused notion of data…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
We introduce a unified sensitivity concept for shape and topological perturbations and perform the sensitivity analysis for a discretized PDE-constrained design optimization problem in two space dimensions. We assume that the design is…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
Identifiability means that iterates generated by optimization algorithms are eventually confined to an identifiable set. This property is computationally useful because minimizing a nonsmooth function near a critical point reduces to…
Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…