An integer programming model for the truck dock assignment problem with operational time constraint within cross docks has been proposed in (Miao, Z.,Lim, A.,Ma, H., 2009. Truck dock assignment problem with operational time constraint within crossdocks. European Journal of Operational Research 192 (1), 105–115). We address the following issues in this formulation: 1) from among … Read more
We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net support vector machine (SVM) through an alternating direction method of multipliers in the first phase, followed by an interior-point method … Read more
The p-facility Huff location problem aims at locating facilities on a competitive environment so as to maximize the market share. While it has been deeply studied in the field of continuous location, in this paper we study the p-facility Huff location problem on networks formulated as a Mixed Integer Nonlinear Programming problem that can be … Read more
This is a survey on the infinite group problem, an infinite-dimensional relaxation of integer linear optimization problems introduced by Ralph Gomory and Ellis Johnson in their groundbreaking papers titled “Some continuous functions related to corner polyhedra I, II” [Math. Programming 3 (1972), 23-85, 359-389]. The survey presents the infinite group problem in the modern context … Read more
Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phenomena, by relaxing controls as Young measures. These semi-definite relaxations were later on extended to optimal control problems depending linearly on the control input and typically featuring concentration phenomena, interpreting the control as a measure of time with a … Read more
The service system design problem arises in the design of telecommunication networks, refuse collection and disposal networks in public sector, transportation planning, and location of emergency medical facilities. The problem seeks to locate service facilities, determine their capacities and assign users to those facilities under time varying demand conditions. The objective is to minimize total … Read more
We propose primal-dual active-set (PDAS) methods for solving large-scale instances of an important class of convex quadratic optimization problems (QPs). The iterates of the algorithms are partitions of the index set of variables, where corresponding to each partition there exist unique primal-dual variables that can be obtained by solving a (reduced) linear system. Algorithms of … Read more
For index-based hedging design, the scatter plot of the hedging contract losses versus the losses to be hedged is generally used to visualize and quantify basis risk. While studying this scatter plot, which does not cluster along the diagonal as desired, a “bundled loss” phenomenon is found. In a setting where both the hedging and … Read more
We develop a natural variant of Dikin’s affine-scaling method, first for semidefinite programming and then for hyperbolic programming in general. We match the best complexity bounds known for interior-point methods. All previous polynomial-time affine-scaling algorithms have been for conic optimization problems in which the underlying cone is symmetric. Hyperbolicity cones, however, need not be symmetric. … Read more
In this paper we consider the notion of rectangularity of a set of probability measures, introduced in Epstein and Schneider (2003), from a somewhat different point of view. We define rectangularity as a property of dynamic decomposition of a distributionally robust stochastic optimization problem and show how it relates to the modern theory of coherent … Read more