For continuous decision spaces, nonlinear programs (NLPs) can be efficiently solved via sequential quadratic programming (SQP) and, more generally, sequential convex programming (SCP). These algorithms linearize only the nonlinear equality constraints and keep the outer convex structure of the problem intact, such as (conic) inequality constraints or convex objective terms. The aim of the presented … Read more
Network design problems involve constructing edges in a transportation or supply chain network to minimize construction and daily operational costs. We study a stochastic version where operational costs are uncertain due to fluctuating demand and estimated as a sample average from historical data. This problem is computationally challenging, and instances with as few as 100 … Read more
This paper studies a variant of the traveling salesman problem called the pickup-and-delivery traveling salesman problem with neighborhoods that combines traditional pickup and delivery requirements with the flexibility of visiting the customers at locations within compact neighborhoods of arbitrary shape. We derive two optimality conditions for the problem, a local condition that verifies whether a … Read more
A frequently studied problem in the context of digital marketing for online social networks is the influence maximization problem that seeks for an initial seed set of influencers to trigger an information propagation cascade (in terms of active message forwarders) of expected maximum impact. Previously studied problems typically neglect that the probability that individuals passively … Read more
In this paper, we propose a generalized Benders decomposition-based branch and bound algorithm, GBDBAB, to solve two-stage convex 0-1 mixed-integer nonlinear stochastic programs with mixed-integer variables in both first and second stage decisions. In order to construct the convex hull of the MINLP subproblem for each scenario in closed-form, we first represent each MINLP subproblem … Read more
Mathematical modeling of market design issues in liberalized electricity markets often leads to mixed-integer nonlinear multilevel optimization problems for which no general-purpose solvers exist and which are intractable in general. In this work, we consider the problem of splitting a market area into a given number of price zones such that the resulting market design … Read more
This paper focuses on transportation network protection to hedge against extreme events such as earthquakes. Traditional two-stage stochastic programming has been widely adopted to obtain solutions under a risk-neutral preference through the use of expectations in the recourse function. In reality, decision makers hold different risk preferences. We develop a mean-risk two-stage stochastic programming model … Read more
In the context of convex mixed-integer nonlinear programming (MINLP), we investigate how the outer approximation method and the generalized Benders decomposition method are affected when the respective NLP subproblems are solved inexactly. We show that the cuts in the corresponding master problems can be changed to incorporate the inexact residuals, still rendering equivalence and finiteness … Read more
In the context of convex mixed-integer nonlinear programming (MINLP), we investigate how the outer approximation method and the generalized Benders decomposition method are affected when the respective NLP subproblems are solved inexactly. We show that the cuts in the corresponding master problems can be changed to incorporate the inexact residuals, still rendering equivalence and finiteness … Read more