Related papers: Perturbation Analysis of Singular Semidefinite Pro…
A basic requirement for a mathematical model is often that its solution (output) shouldn't change much if the model's parameters (input) are perturbed. This is important because the exact values of parameters may not be known and one would…
When we speak about parametric programming, sensitivity analysis, or related topics, we usually mean the problem of studying specified perturbations of the data such that for a given optimization problem some optimality criterion remains…
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
In this paper, we extend the idea of using controlled perturbations to enhance the capabilities of active-set prediction for interior point methods for convex Quadratic Programming (QP) problems. Namely, we consider perturbing the…
Stability of nonconvex quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces is investigated. We present several stability properties of the global solution map, and the continuity of the optimal…
Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…
Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over continuous time. We analyse this problem with respect to the allowable control sets, which are assumed to be the image under a linear…
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 work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable…
Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…
In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
In this paper, we propose a novel framework for approximating the explicit MPC law for linear parameter-varying systems using supervised learning. In contrast to most existing approaches, we not only learn the control policy, but also a…
A defective eigenvalue is well documented to be hypersensitive to data perturbations and round-off? errors, making it a formidable challenge in numerical computation particularly when the matrix is known through approximate data. This paper…
This paper studies the problem of perturbed convex and smooth optimization. The main results describe how the solution and the value of the problem change if the objective function is perturbed. Examples include linear, quadratic, and…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…
We discuss how semidefinite programming can be used to determine the second-order density matrix directly through a variational optimization. We show how the problem of characterizing a physical or N -representable density matrix leads to…
The paper concerns multiobjective linear optimization problems in R^n that are parameterized with respect to the right-hand side perturbations of inequality constraints. Our focus is on measuring the variation of the feasible set and the…