Related papers: Linear programming sensitivity measured by the opt…
This paper presents a novel sensitivity-based distributed programming (SBDP) approach for non-convex, large-scale nonlinear programs (NLP). The algorithm relies on first-order sensitivities to cooperatively solve the central NLP in a…
In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations…
While the design of optimal peak-to-peak controllers/observers for linear systems is known to be a difficult problem, this problem becomes interestingly much easier in the context of interval observers because of the positive nature of the…
A common goal throughout science and engineering is to solve optimization problems constrained by computational models. However, in many cases a high-fidelity numerical emulation of systems cannot be optimized due to code complexity and…
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
This paper addresses the problem of estimating multiplicative fault signals in linear time-invariant systems by processing its input and output variables, as well as designing an input signal to maximize the accuracy of such estimates. The…
We study the computational complexity of decision problems in $k$-level linear programming (LP). Seminal work by Jeroslow establishes that determining whether the optimal objective value of a $k$-level LP is at least as good as a given…
Multilevel programming is the standard framework for modeling hierarchical decision-making. In this paper, we characterize the computational complexity of deciding the existence of feasible and optimal solutions, as well as computing the…
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…
In this paper we shall review the common problems associated with Piecewise Linear Separation incremental algorithms. This kind of neural models yield poor performances when dealing with some classification problems, due to the evolving…
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…
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…
In this article, we introduce a new technique for precision tuning. This problem consists of finding the least data types for numerical values such that the result of the computation satisfies some accuracy requirement. State of the art…
Sensitivity-based distributed programming (SBDP) is a decomposition method for solving large-scale nonlinear programs over graph-structured networks. However, its convergence depends on the strength and structure of subsystem coupling. To…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
We consider learning problems of an intuitive and concise preference model, called lexicographic preference lists (LP-lists). Given a set of examples that are pairwise ordinal preferences over a universe of objects built of attributes of…
A study of the greatest possible ratio of the smallest absolute value of a higher derivative of some function, defined on a bounded interval, to the L p-norm of the function.
In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…
We consider a general linear program in standard form whose right-hand side constraint vector is subject to random perturbations. This defines a stochastic linear program for which, under general conditions, we characterize the fluctuations…
We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand-side of the constraint system and the vector defining the objective function are subject to change. Using…