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We propose an extended variant of the reformulation and decomposition algorithm for solving a special class of mixed-integer bilevel linear programs (MIBLPs) where continuous and integer variables are involved in both upper- and lower-level…
We study discrete probabilistic programs with potentially unbounded looping behaviors over an infinite state space. We present, to the best of our knowledge, the first decidability result for the problem of determining whether such a…
We study a Q learning algorithm for continuous time stochastic control problems. The proposed algorithm uses the sampled state process by discretizing the state and control action spaces under piece-wise constant control processes. We show…
We develop a framework for approximation limits of polynomial-size linear programs from lower bounds on the nonnegative ranks of suitably defined matrices. This framework yields unconditional impossibility results that are applicable to any…
This papers deals with the constrained discounted control of piecewise deterministic Markov process (PDMPs) in general Borel spaces. The control variable acts on the jump rate and transition measure, and the goal is to minimize the total…
This paper addresses the problem of tightening the mixed-integer linear programming (MILP) formulation for continuous piecewise linear (CPWL) approximations of data sets in arbitrary dimensions. The MILP formulation leverages the…
Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods. A PDMP is…
We establish a linear programming formulation for the solution of joint chance constrained optimal control problems over finite time horizons. The joint chance constraint may represent an invariance, reachability or reach-avoid…
Machine Learning models are increasingly used for decision making, in particular in high-stakes applications such as credit scoring, medicine or recidivism prediction. However, there are growing concerns about these models with respect to…
We consider nonlinear optimal control problems (OCPs) for which all problem data are polynomial. In the first part of the paper, we review how occupation measures can be used to approximate pointwise the optimal value function of a given…
Phasor Measurement Units (PMUs) are essential measuring devices for monitoring, control and protection of power systems. The objective of the optimal PMU placement (OPP) problem is to minimize the number of PMUs and select the bus locations…
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the…
In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT…
This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…
In this paper, we use the linear programming approach to find new upper bounds for the moments of isotropic measures. These bounds are then utilized for finding lower packing bounds and energy bounds for projective codes. We also show that…
Computing tight over-approximation of reach sets of a controlled uncertain dynamical system is a common practice in verification of safety-critical cyber-physical systems (CPS). While several algorithms are available for this purpose, they…
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…
Discrete time stochastic optimal control problems and Markov decision processes (MDPs), respectively, serve as fundamental models for problems that involve sequential decision making under uncertainty and as such constitute the theoretical…
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…
Machine-learned interatomic potentials (MLIPs) are increasingly used to replace computationally demanding electronic-structure calculations to model matter at the atomic scale. The most commonly used model architectures are constrained to…