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The purpose of this paper is to solve the 0-1 $k$-item quadratic knapsack problem $(kQKP)$, a problem of maximizing a quadratic function subject to two linear constraints. We propose an exact method based on semidefinite optimization. The…
Simulating compositional multiphase flow in porous media is a challenging task, especially when phase transition is taken into account. The main problem with phase transition stems from the inconsistency of the primary variables such as…
Stochastic Optimization is a cornerstone of operations research, providing a framework to solve optimization problems under uncertainty. Despite the development of numerous algorithms to tackle these problems, several persistent challenges…
Various real-world problems consist of partitioning a set of locations into disjoint subsets, each subset spread in a way that it covers the whole set with a certain radius. Given a finite set S, a metric d, and a radius r, define a subset…
Sign-Perturbed Sum (SPS) is a powerful finite-sample system identification algorithm which can construct confidence regions for the true data generating system with exact coverage probabilities, for any finite sample size. SPS was developed…
This work proposes an adaptive sequential Monte Carlo sampling algorithm to solve Bayesian inverse problems in scenarios where likelihood evaluations are costly but can be approximated using a surrogate model built from previous evaluations…
We consider the chance-constrained binary knapsack problem (CKP), where the item weights are independent and normally distributed. We introduce a continuous relaxation for the CKP, represented as a non-convex optimization problem, which we…
We prove two sharp estimates for the subspace of a standard weighted Bergman space that consists of functions vanishing at a given point (with prescribed multiplicity).
We present a methodology for bounding the error term of an asymptotic solution to a singularly perturbed optimal control (SPOC) problem whose exact solution is known to be computationally intractable. In previous works, reduced or…
An important problem in space-time adaptive detection is the estimation of the large p-by-p interference covariance matrix from training signals. When the number of training signals n is greater than 2p, existing estimators are generally…
Schaefer's dichotomy theorem [Schaefer, STOC'78] states that a boolean constraint satisfaction problem (CSP) is polynomial-time solvable if one of six given conditions holds for every type of constraint allowed in its instances. Otherwise,…
Conformal prediction (CP) is a method for constructing a prediction interval around the output of a fitted model, whose validity does not rely on the model being correct--the CP interval offers a coverage guarantee that is…
Marginal Structural Models (MSM) are the most popular models for causal inference from time-series observational data. However, they have two main drawbacks: (a) they do not capture subject heterogeneity, and (b) they only consider fixed…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
This paper looks at the tensor eigenvalue complementarity problem (TEiCP) which arises from the stability analysis of finite dimensional mechanical systems and is closely related to the optimality conditions for polynomial optimization. We…
Many natural optimization problems derived from $\sf NP$ admit bilevel and multilevel extensions in which decisions are made sequentially by multiple players with conflicting objectives, as in interdiction, adversarial selection, and…
In this paper, some preliminaries about Morgan problem, signal flow graph and controllable linear time-invariant standard system are first introduced in detail. In order to synthesize the necessary and sufficient condition for decoupling…
The rational covariance extension problem (RCEP) is an important problem in systems and control occurring in such diverse fields as control, estimation, system identification, and signal and image processing, leading to many fundamental…
Schr\"{o}dinger bridge is a stochastic optimal control problem to steer a given initial state density to another, subject to controlled diffusion and deadline constraints. A popular method to numerically solve the Schr\"{o}dinger bridge…
We consider a non-polynomial cubic spline to develop the classes of methods for the numerical solution of singularly perturbed two-point boundary value problems. The proposed methods are second and fourth order accurate and applicable to…