The risk-averse ultimate pit problem

In this work, we consider a risk-averse ultimate pit problem where the grade of the mineral is uncertain. We propose a two-stage formulation of the problem and discuss which properties are desirable for a risk measure in this context. We show that the only risk measure that satisfies these properties is the entropic. We propose … Read more

On the existence of a short pivoting sequence for a linear program

Pivoting methods are of vital importance for linear programming, the simplex method being the by far most well-known. In this paper, a primal-dual pair of linear programs in canonical form is considered. We show that there exists a sequence of pivots, whose length is bounded by the minimum dimension of the constraint matrix, such that … Read more

Domain-Driven Solver (DDS): a MATLAB-based Software Package for Convex Optimization Problems in Domain-Driven Form

Domain-Driven Solver (DDS) is a MATLAB-based software package for convex optimization problems in Domain-Driven form [11]. The current version of DDS accepts every combination of the following function/set constraints: (1) symmetric cones (LP, SOCP, and SDP); (2) quadratic constraints; (3) direct sums of an arbitrary collection of 2-dimensional convex sets defined as the epigraphs of … Read more

Representation of the Pareto front for heterogeneous multi-objective optimization

Optimization problems with multiple objectives which are expensive, i.e. where function evaluations are time consuming, are difficult to solve. Finding at least one locally optimal solution is already a difficult task. In case only one of the objective functions is expensive while the others are cheap, for instance analytically given, this can be used in … Read more

On the intrinsic core of convex cones in real linear spaces

Convex cones play an important role in nonlinear analysis and optimization theory. In particular, specific normal cones and tangent cones are known to be convex cones, and it is a crucial fact that they are useful geometric objects for describing optimality conditions. As important applications (especially, in the fields of optimal control with PDE constraints, … Read more

Weak sharpness and finite termination for variational inequalities on Hadamard manifolds

We first introduce the notion of weak sharpness for the solution sets of variational inequality problems (in short, VIP) on Hadamard spaces. We then study the finite convergence property of sequences generated by the inexact proximal point algorithm with different error terms for solving VIP under weak sharpness of the solution set. We also give … Read more

Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely many training samples that will perform well on unseen test samples. This learning task is difficult even if all training and test … Read more

A New Sequential Updating Scheme of the Lagrange Multiplier for Multi-Block Linearly Constrained Separable Convex Optimization with Relaxed Step Sizes

In various applications such as signal/image processing, data mining, statistical learning and etc., the multi-block linearly constrained separable convex optimization is frequently used, where the objective function is the sum of multiple individual convex functions, and the major constraints are linear. A classical method for solving such kind of optimization problem could be the alternating … Read more

Branch-and-Cut-and-Price for Multi-Agent Pathfinding

There are currently two broad strategies for optimal Multi-agent Pathfinding (MAPF): (1) search-based methods, which model and solve MAPF directly, and (2) compilation-based solvers, which reduce MAPF to instances of well-known combinatorial problems, and thus, can benefit from advances in solver techniques. In this work, we present an optimal algorithm, BCP, that hybridizes both approaches … Read more

Tractable Reformulations of Distributionally Robust Two-stage Stochastic Programs with $\infty- Distance

In the optimization under uncertainty, decision-makers first select a wait-and-see policy before any realization of uncertainty and then place a here-and-now decision after the uncertainty has been observed. Two-stage stochastic programming is a popular modeling paradigm for the optimization under uncertainty that the decision-makers first specifies a probability distribution, and then seek the best decisions … Read more