In this technical note, a novel single-layer inverse-free fixed-time dynamical system (SIFDS) is proposed to address absolute value equations. The proposed SIFDS directly employs coefficient matrix and absolute value equation function that aims at circumventing matrix inverse operation and achieving fixed-time convergence. The equilibria of the proposed SIFDS is proved to be the unique solution … Read more
In this paper, we study distributionally risk-receptive and distributionally robust (or risk-averse) multistage stochastic mixed-integer programs (denoted by DRR- and DRO-MSIPs). We present cutting plane-based and reformulation-based approaches for solving DRR- and DRO-MSIPs without and with decision-dependent uncertainty to optimality. We show that these approaches are finitely convergent with probability one. Furthermore, we introduce generalizations … Read more
Let X1, X2, . . . , Xn be n independent and uniformly distributed random points in a compact region R ⊂ R2 of area 1. Let TSP(X1, . . . , Xn) denote the length of the optimal Euclidean traveling salesman tour that traverses all these points. The classical Beardwood-Halton-Hammersley theorem proves the existence … Read more
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show similar results for a wide variety of discrete optimization problems for which SDP relaxations have been derived. Based on a … Read more
We present a branch-and-bound method for multiobjective mixed-integer convex quadratic programs that computes a superset of efficient integer assignments and a coverage of the nondominated set. The method relies on outer approximations of the upper image set of continuous relaxations. These outer approximations are obtained addressing the dual formulations of specific subproblems where the values … Read more
The robust multi-product pricing problem is to determine the prices of a collection of products so as to maximize the worst-case revenue, where the worst case is taken over an uncertainty set of demand models that the firm expects could be realized in practice. A tacit assumption in this approach is that the pricing decision … Read more
Having in mind singular solutions of smooth reformulations of complementarity problems, arising unavoidably when the solution in question violates strict complementarity, we study the behavior of Newton-type methods near singular solutions of nonlinear equations, assuming that the operator of the equation possesses a strongly semismooth derivative, but is not necessarily twice differentiable. These smoothness restrictions … Read more
Many liberalized electricity markets use capacity mechanisms to ensure that sufficient resources will be available in advance of operations. Recent events have called into question the ability of capacity mechanisms to provide sufficient incentives for reliability. A core challenge is that penalties for non-performance on capacity obligations are lower than what theory would suggest is … Read more
We consider robust submodular maximization problems (RSMs), where given a set of \(m\) monotone submodular objective functions, the robustness is with respect to the worst-case (scaled) objective function. The model we consider generalizes two variants of robust submodular maximization problems in the literature, depending on the choice of the scaling vector. On one hand, by using … Read more
The backtracking line-search is an effective technique to automatically tune the step-size in smooth optimization. It guarantees similar performance to using the theoretically optimal step-size. Many approaches have been developed to instead tune per-coordinate step-sizes, also known as diagonal preconditioners, but none of the existing methods are provably competitive with the optimal per-coordinate stepsizes. We … Read more