In this paper, an algorithm is proposed to find the nearest point of a convex cone to a given vector, which is composed of a series of orthogonal projections. Some properties of this algorithm, including the reasonability of implementation, the global convergence property and the finite termination, etc., are obtained. The proposed algorithm is more … Read more
We study the problem of strategically eliciting the preferences of a decision-maker through a moderate number of pairwise comparison queries with the goal of making them a high quality recommendation for a specific decision-making problem. We are particularly motivated by applications in high stakes domains, such as when choosing a policy for allocating scarce resources … Read more
We propose, implement, and test two approaches for dispatching trucks in an open-pit mining operation. The first approach relies on a nonlinear optimization model that incorporates queueing effects to set target average flow rates between mine locations. The second approach is based on a time-discretized mixed integer programming (MIP) model. The MIP model is difficult … Read more
The problem of minimizing a (nonconvex) quadratic form over the unit simplex, referred to as a standard quadratic program, admits an exact convex conic formulation over the computationally intractable cone of completely positive matrices. Replacing the intractable cone in this formulation by the larger but tractable cone of doubly nonnegative matrices, i.e., the cone of … Read more
This paper deals with a general framework for inexact forward–backward algorithms aimed at minimizing the sum of an analytic function and a lower semicontinuous, subanalytic, convex term. Such framework relies on an implementable inexactness condition for the computation of the proximal operator, and a linesearch procedure which is possibly performed whenever a variable metric is … Read more
In this paper we consider stochastic weakly convex composite problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient estimate of the smoothed function. We prove convergence at a similar rate as state of the art methods, however with … Read more
We give safe screening rules to eliminate variables from regression with L0 regularization or cardinality constraint. These rules are based on guarantees that a feature may or may not be selected in an optimal solution. The screening rules can be computed from a convex relaxation solution in linear time, without solving the L0 optimization problem. … Read more
For solving structured monotone inclusion problems involving the sum of finitely many maximal monotone operators, we propose and study a relative-error inertial-relaxed inexact projective splitting algorithm. The proposed algorithm benefits from a combination of inertial and relaxation effects, which are both controlled by parameters within a certain range. We propose sufficient conditions on these parameters … Read more
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixed-integer programming (MIP) technology. Yet, existing approaches from the literature do not leverage the power of MIP to its full extent. Indeed, … Read more
We consider an integrated pricing and routing problem on a network. The problem is motivated by applications in freight transportation such as package delivery and less-than-truckload shipping services. The decision maker sets a price for each origin-destination pair of the network, which determines the demand flow that needs to be served. The flows are then … Read more