Related papers: Robust Sensitivity Analysis of the Optimal Value o…
This paper introduces a concept of a derivative of the optimal value function in linear programming (LP). Basically, it is the the worst case optimal value of an interval LP problem when the nominal data the data are inflated to intervals…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
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…
Absolute value linear programming problems is quite a new area of optimization problems, involving linear functions and absolute values in the description of the model. In this paper, we consider interval uncertainty of the input…
In this paper, we provide an elementary, geometric, and unified framework to analyze conic programs that we call the strict complementarity approach. This framework allows us to establish error bounds and quantify the sensitivity of the…
This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number…
This paper studies an integrated learning and optimization problem in which a prediction model estimates the right-hand-side parameters of a linear program (LP) using a contextual vector. Considering that such a prediction alters the…
We study a worst-case approach to measure the sensitivity to model misspecification in the performance analysis of stochastic systems. The situation of interest is when only minimal parametric information is available on the form of the…
We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. We show how an integrality gap verifier for the linear programming relaxation of the non-robust version of the problem can be…
Given a family of linear constraints and a linear objective function one can consider whether to apply a Linear Programming (LP) algorithm or use a Linear Superiorization (LinSup) algorithm on this data. In the LP methodology one aims at…
We consider ILPs, where each variable corresponds to an integral point within a polytope $\mathcal{P}$, i. e., ILPs of the form $\min\{c^{\top}x\mid \sum_{p\in\mathcal P\cap \mathbb Z^d} x_p p = b, x\in\mathbb Z^{|\mathcal P\cap \mathbb…
It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…
In this paper, we present a new geometric approach for sensitivity analysis in linear programming that is computationally practical for a decision-maker to study the behavior of the optimal solution of the linear programming problem under…
Robust optimization is a framework for modeling optimization problems involving data uncertainty and during the last decades has been an area of active research. If we focus on linear programming (LP) problems with i) uncertain data, ii)…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
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…
Sensitivity analysis plays a crucial role in multiobjective linear programming (MOLP), where understanding the impact of parameter changes on efficient solutions is essential. This work builds upon and extends previous investigations. In…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…
It has been verified that the linear programming (LP) is able to formulate many real-life optimization problems, which can obtain the optimum by resorting to corresponding solvers such as OptVerse, Gurobi and CPLEX. In the past decades, a…