The critical node selection problem (CNP) has important applications in telecommunication, supply chain design, and disease propagation prevention. In practice, the weights on the connections are either uncertain or hard to estimate so recently robust optimization approaches have been considered for CNP. In this article, we address very general uncertainty sets, only requiring a linear … Read more
We present an infeasible primal-dual interior point method for semidefinite optimization problems, making use of constraint reduction. We show that the algorithm is globally convergent and has polynomial complexity, the first such complexity result for primal-dual constraint reduction algorithms for any class of problems. Our algorithm is a modification of one with no constraint reduction … Read more
We give a comprehensive theoretical treatment for calculating the viewshed of a given point, present an analytical solution to the viewshed problem and a new algorithm for finding the viewshed on a triangulated terrain. We implement our algorithm on a real terrain. Some algorithms make use of the horizon information of the terrain to calculate … Read more
We study the practical production planning problem of a food producer facing a non-stationary erratic demand for a perishable product with a fixed life time. In meeting the uncertain demand, the food producer uses a FIFO issuing policy. The food producer aims at meeting a certain service level at lowest cost. Every production run a … Read more
We introduce a new flexible Inexact-Restoration (IR) algorithm and an application to problems with multiobjective constraints (MOCP) under the weighted-sum scalarization approach. In IR methods each iteration has two phases. In the first phase one aims to improve the feasibility and, in the second phase, one minimizes a suitable objective function. This is done in … Read more
This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but convex) component. In order to solve these problems, we propose a randomized stochastic projected gradient (RSPG) algorithm, in which proper mini-batch of samples are … Read more
A spectrahedron is the positivity region of a linear matrix pencil, thus defining the feasible set of a semidefinite program. We propose and study a hierarchy of sufficient semidefinite conditions to certify the containment of a spectrahedron in another one. This approach comes from applying a moment relaxation to a suitable polynomial optimization formulation. The … Read more
We present a sequential quadratic optimization (SQO) algorithm for nonlinear constrained optimization. The method attains all of the strong global and fast local convergence guarantees of classical SQO methods, but has the important additional feature that fast local convergence is guaranteed when the algorithm is employed to solve infeasible instances. A two-phase strategy, carefully constructed … Read more
We propose a distributed positioning algorithm to estimate the unknown positions of a number of target nodes, given distance measurements between target nodes and between target nodes and a number of reference nodes at known positions. Based on a geometric interpretation, we formulate the positioning problem as an implicit convex feasibility problem in which some … Read more
This paper is on the portfolio optimization problem for which two generic models are presented in the context of a proprietary solver called GENO: the first is a pseudo-dynamic model meant for the single holding-period case; the second is a truly dynamic model that applies to both the single and the multi-period scenario. Both models … Read more