Related papers: Continuity in Parametric Linear Programming
Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not…
In this paper, we define the upper (resp. lower) covariance under multiple probabilities via a corresponding max-min-max (resp. min-max-min) optimization problem and the related properties of covariances are obtained. In particular, we…
For an $n$-by-$n$ matrix $A$, let $f_A$ be its "field of values generating function" defined as $f_A\colon x\mapsto x^*Ax$. We consider two natural versions of the continuity, which we call strong and weak, of $f_A^{-1}$ (which is of course…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
Over the last two decades, submodular function maximization has been the workhorse of many discrete optimization problems in machine learning applications. Traditionally, the study of submodular functions was based on binary function…
While known algorithms for sensitivity analysis and parameter tuning in probabilistic networks have a running time that is exponential in the size of the network, the exact computational complexity of these problems has not been established…
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…
We prove the continuity of the value function of the sparse optimal control problem. The sparse optimal control is a control whose support is minimum among all admissible controls. Under the normality assumption, it is known that a sparse…
This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications…
The paper provides a thorough comparison between R-continuity and other fundamental tools in optimization such as metric regularity, metric subregularity and calmness. We show that R-continuity has some advantages in the convergence rate…
Our model is a generalized linear programming relaxation of a much studied random K-SAT problem. Specifically, a set of linear constraints C on K variables is fixed. From a pool of n variables, K variables are chosen uniformly at random and…
The addition of lower level integrality constraints to a bi-level linear program is known to result in significantly weaker analytical properties. Most notably, the upper level goal function in the optimistic setting lacks lower…
Dependence on the parameter is continuous when perturbations of the parameter preserves strict preference for one alternative over another. We characterise this property via a utility function over alternatives that depends continuously on…
In this paper we examine multi-objective linear programming problems in the face of data uncertainty both in the objective function and the constraints. First, we derive a formula for radius of robust feasibility guaranteeing constraint…
We introduce an extension of decision problems called resiliency problems. In resiliency problems, the goal is to decide whether an instance remains positive after any (appropriately defined) perturbation has been applied to it. To tackle…
The goal of this paper is to investigate new and simple convergence analysis of dynamic programming for linear quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of…
We study the continuity of many channel parameters and operations under various topologies on the space of equivalent discrete memoryless channels (DMC). We show that mutual information, channel capacity, Bhattacharyya parameter,…
We examine robust output feedback control of discrete-time nonlinear systems with bounded uncertainties affecting the dynamics and measurements. Specifically, we demonstrate how to construct semi-infinite programs that produce gains to…
In this paper, we investigate the continuity of linear and sublinear correspondences defined on cones in normed spaces. We also generalize some known results for sublinear correspondences.
This work shows the existence of optimal control laws for persistent monitoring of mobile targets in a one-dimensional mission space and derives explicit solutions. The underlying performance metric consists of minimizing the total…