In this paper, a new method for determining all minimal representations of a face of a polyhedron is proposed. A main difficulty for determining prime and minimal representations of a face is that the deletion of one redundant constraint can change the redundancy of other constraints. To reduce computational efforts in finding all minimal representations … Read more
Rapid urban growth, the increasing importance of e-commerce and high consumer service expectations have given rise to new and innovative models for freight delivery within urban environments. Crowdsourced solutions – where drivers are not employed by a carrier but occasionally offer their services through on-line platforms and are contracted as required by carriers – are … Read more
We investigate an algorithm of gradient type with a backward inertial step in connection with the minimization of a nonconvex differentiable function. We show that the generated sequences converge to a critical point of the objective function, if a regularization of the objective function satis es the Kurdyka-Lojasiewicz property. Further, we provide convergence rates for the … Read more
The field of Combinatorial Optimization (CO) is one of the most important areas in the general field of optimization, with important applications found in every industry, including both the private and public sectors. It is also one of the most active research areas pursued by the research communities of Operations Research, Computer Science, and Analytics … Read more
The Intentional Controlled Islanding (ICI) and the Black Start Allocation (BSA) are two examples of problems in the power systems literature that have been formulated as Mixed Integer Programs (MIPs). A key consideration in both of these problems is that each island must have at least one energized generator. In this paper, we provide three … Read more
The separable convex resource allocation problem with nested bound constraints aims to allocate $B$ units of resources to $n$ activities to minimize a separable convex cost function, with lower and upper bounds on the total amount of resources that can be consumed by nested subsets of activities. We develop a new combinatorial algorithm to solve … Read more
In this study we discuss the use of the simplex method to solve allocation problems whose flow matrices are doubly stochastic. Although these problems can be solved via a 0-1 integer programming method, H.W. Kuhn [4] suggested the use of linear programming in addition to the Hungarian method. Specifically, we use the Birkhoff’s theorem to … Read more
We consider combinatorial optimization problems with uncertainty in the cost vector. Recently a novel approach was developed to deal such uncertainties: instead of a single one robust solution, obtained by solving a min max problem, the authors consider a set of solutions obtained by solving a min max min problem. In this new approach the … Read more
The influence maximization problem (IMP) aims to determine the most influential individuals within a social network. In this study first we develop a binary integer program that approximates the original problem by Monte Carlo sampling. Next, to solve IMP efficiently, we propose a linear programming relaxation based method with a provable worst case bound that … Read more
In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming only the knowledge of the mean and the covariance matrix entries restricted to block-diagonal patterns, we develop a reduced semidefinite programming formulation, … Read more