We study cyclic binary strings with bounds on the lengths of the intervals of consecutive ones and zeros. This is motivated by scheduling problems where such binary strings can be used to represent the state (on/off) of a machine. In this context the bounds correspond to minimum and maximum lengths of on- or off-intervals, and … Read more
In the last two decades, many descent methods for multiobjective optimization problems were proposed. In particular, the steepest descent and the Newton methods were studied for the unconstrained case. In both methods, the search directions are computed by solving convex subproblems, and the stepsizes are obtained by an Armijo-type line search. As a consequence, the … Read more
We propose a novel theoretical framework to investigate deep neural networks using the formalism of proximal fixed point methods for solving variational inequalities. We first show that almost all activation functions used in neural networks are actually proximity operators. This leads to an algorithmic model alternating firmly nonexpansive and linear operators. We derive new results … Read more
We establish a general computational framework for Chvátal’s conjecture based on exact rational integer programming. As a result we prove Chvátal’s conjecture holds for all downsets whose union of sets contains seven elements or less. The computational proof relies on an exact branch-and-bound certificate that allows for elementary verification and is independent of the integer … Read more
We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and backward passes of the method are solved with bounded errors (inexactly). This inexact variant of SDDP is described both for … Read more
In this paper, we discuss input modeling and solution techniques for several classes of chance constrained programs (CCPs). We propose to use Gaussian mixture models (GMM), a semi-parametric approach, to fit the data available and to model the randomness. We demonstrate the merits of using GMM. We consider several scenarios that arise from practical applications … Read more
We explore optimization models to support the planning and operations functions at package express carriers in China. The models simultaneously consider ground and air transportation, company-owned and purchased capacity, multiple service products, and shipments becoming available throughout the day. An extensive computational study using real-life data shows the efficacy of the models, provides insights into … Read more
Bellman formulated a vague principle for optimization over time, which characterizes optimal policies by stating that a decision maker should not regret previous decisions retrospectively. This paper addresses time consistency in stochastic optimization. The problem is stated in generality first. The paper discusses time consistent decision-making by addressing risk measures which are recursive, nested, dynamically … Read more
We consider the best subset selection problem in linear regression, i.e., finding a parsimonious subset of the regression variables that provides the best fit to the data according to some predefined criterion. We show that, for a broad range of criteria used in the statistics literature, the best subset selection problem can be modeled as … Read more
This paper studies a stochastic congested location problem in the network of a service system that consists of facilities to be established in a finite number of candidate locations. Population zones allocated to each open service facility together creates a stream of demand that follows a Poisson process and may cause congestion at the facility. … Read more