A new Block Coordinate Gradient (BCG) method, dubbed bAdag, for smooth, nonconvex minimization problem is proposed; it falls in the class of Objective Function Free Optimization (OFFO) methods, and it is based on the AdaGrad algorithm. At each iteration, our method computes an adaptive step size based on the cumulative sum of block gradients, instead … Read more
The superiorization method (SM) is situated between feasibility-seeking and constrained optimization. Instead of aiming at the minimum of a given objective function over a constraint set, it seeks a feasible point at which the objective function value is reduced — though not necessarily minimal — compared to that reached by the feasibility-seeking algorithm alone. This … Read more
We use symmetric gauge theory to develop a general class of cutting-plane algorithms for semidefinite programming. We formulate a separation problem based on spectral normalizations induced by gauges and derive a closed-form separation oracle. This oracle yields an implementable cut-generation procedure that, by varying the gauge, recovers standard cut families and generates new ones with … Read more
We study the convex hull obtained after deleting prescribed vertices from the binary cube. The analysis separates three regimes according to the number of deleted vertices. When this number is fixed, both the original-space facet count and the linear extension complexity remain linear in the ambient dimension, up to constants depending only on the number … Read more
Human activities increasingly fragment natural habitats, placing many species at risk of population decline. This creates an urgent need to preserve biodiversity and maintain ecological connectivity through wildlife corridors. We present two spatial optimization models for corridor design that explicitly incorporate corridor width as a key ecological criterion. The first model minimizes total corridor cost … Read more
Network design problems increasingly arise in settings where strategic infrastructure decisions and operational routing choices are made by different actors. Such interactions are naturally modeled as bilevel problems: a network operator designs or modifies a network, while users respond by selecting routes according to their own utilities. This structure captures many applications in transportation and … Read more
In this paper, we propose and analyze a globally convergent regularized Newton method with positive definite regularization for solving nonsmooth optimization problems. Our approach leverages the coderivative-generated second-order subdifferential (generalized Hessian) and replaces the identity matrix in traditional algorithms with a general positive-definite symmetric matrix to regularize the generalized Hessian. By appropriately selecting the regularization … Read more
The global demand for grid-scale energy storage continues to increase. Carnot batteries (CBs) are not geographically constrained and consist of mature components. Furthermore, charging power, discharging power, and storage capacity can be sized independently and tailored to the intended use case. Designing an optimal CB also requires considering the resulting operational behavior. While design and … Read more
The Interval Branch and Bound (IBB) method is a widely used approach for solving nonlinear programming problems, especially when a rigorous solution is required. It uses Interval Arithmetic to handle rounding errors. Although numerous variants of the IBB method have been proposed in the literature, relatively few implementations incorporate Karush-Kuhn-Tucker or Fritz-John (FJ) optimality conditions … Read more
We develop a cutting-plane methodology that adjusts solutions to optimization problems so as to reduce features that bring about exposure to risk, such as concentration of assets or resources. The methodology is agnostic to the representation of risk but has provably good attributes. Our procedure aims to reduce the appropriate risk metric without accruing a … Read more