Mixed 0-1 Linear Programs Under Objective Uncertainty: A Completely Positive Representation

Mixed 0-1 Linear Programs Under Objective Uncertainty: A Completely Positive Representation

In this paper, we analyze mixed 0-1 linear programs under objective uncertainty. The mean vector and the second-moment matrix of the nonnegative objective coefficients are assumed to be known, but the exact form of the distribution is unknown. Our main result shows that computing a tight upper bound on the expected value of a mixed 0-1 linear program in maximization form with random objective i...

Mixed Zero-one Linear Programs under Objective Uncertainty: a Completely Positive Representation

In this paper, we analyze mixed 0-1 linear programs under objective uncertainty. The mean vector and the second moment matrix of the nonnegative objective coefficients is assumed to be known, but the exact form of the distribution is unknown. Our main result shows that computing a tight upper bound on the expected value of a mixed 0-1 linear program in maximization form with random objective is...

Electronic Companion — “ Mixed Zero - One Linear Programs Under Objective Uncertainty : A Completely Positive Representation ”

Bounded Approximations for Linear Multi-Objective Planning Under Uncertainty

Planning under uncertainty poses a complex problem in which multiple objectives often need to be balanced. When dealing with multiple objectives, it is often assumed that the relative importance of the objectives is known a priori. However, in practice human decision makers often find it hard to specify such preferences, and would prefer a decision support system that presents a range of possib...

Deep Neural Networks as 0-1 Mixed Integer Linear Programs: A Feasibility Study

Deep Neural Networks (DNNs) are very popular these days, and are the subject of a very intense investigation. A DNN is made by layers of internal units (or neurons), each of which computes an affine combination of the output of the units in the previous layer, applies a nonlinear operator, and outputs the corresponding value (also known as activation). A commonly-used nonlinear operator is the ...