Optimizing Spatial On-street Parking Provision for Logistic Vehicles
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Month: March 2026
From Computational Certification to Exact Coordinates: Heilbronn’s Triangle Problem on the Unit Square Using Mixed-Integer Optimization
We develop a mixed-integer nonlinear programming (MINLP) approach for the classical Heilbronn triangle problem, demonstrating the capability of modern global optimization solvers to tackle challenging combinatorial geometry problems. A symmetry-breaking strategy based on boundary structure yields a substantially stronger model: for n=9, we compute an epsilon-globally optimal point in 15 minutes on a standard desktop … Read more
Zimpler – Integer Programming, easier
This paper introduces Zimpler, a free tool built on the ZIMPL modeling language to streamline the solution of mixed-integer linear programs (MILP). Zimpler extends existing ZIMPL workflows by integrating native data sources—such as Excel spreadsheets—without requiring manual conversion to text-based tables. In addition, it supports solution refinement by adapting solver outputs into alternative formats, including … Read more
A Multi-Secant Limited-Memory BFGS Method
We develop multi-secant BFGS-like quasi-Newton updating scheme, which adaptively selects the number of imposed secant conditions and naturally preserves positivity of approximated Hessian. Compact representation and respective limited-memory formulation are also derived. Numerical stability is assured via unconventional damping technique, which symmetrically handles coordinate and gradient differences. Practical relevance of proposed method is demonstrated via … Read more
Water network design and operation optimization: Leveraging approximations
This study concerns the optimal design and operation of produced water and urban water networks. The optimization formulations of these problems have inherent nonconvexity, making them hard to solve. We address a key source of nonconvexity and difficulty in solving these problems: the representation of frictional pressure changes across network nodes using nonlinear constraints, typically … Read more
Fair Vehicle Routing via Bilevel Optimization
We propose a novel approach to modeling fairness in the Vehicle Routing Problem (VRP) by introducing objective functions based on ordering route lengths, capturing both monotonic and non-monotonic equity measures. Our method ensures allocations that are efficient, capacity-feasible, and equitable according to criteria like min-max, range, Gini, variance, or absolute deviations. To prevent biased or … Read more
Branch-and-Cut for Mixed-Integer Linear Decision-Dependent Robust Optimization
Decision-dependent robust optimization (DDRO) problems are usually tackled by reformulating them using a strong-duality theorem for the uncertainty set model. If the uncertainty set is, however, described by a mixed-integer linear model, dualization techniques cannot be applied and the literature on solution methods is very scarce. In this paper, we exploit the equivalence of DDRO … Read more
A Modified Projected Gradient Algorithm for Solving Quasiconvex Programming with Applications
In this manuscript, we introduce a novel projected gradient algorithm for solving quasiconvex optimization problems over closed convex sets. The key innovation of our new algorithm is an adaptive, parameter-free stepsize rule that requires no line search and avoids estimating constants, such as Lipschitz modulus. Unlike recent self-adaptive approach given in [17] which typically produce … Read more
Risk-Averse Stochastic User Equilibrium on Uncertain Transportation Networks
Extreme weather events, like flooding, disrupt urban transportation networks by reducing speeds and capacities, and by closing roadways. These hazards create regime-dependent uncertainty in link performance and travel-time distribution tails, challenging conventional traffic assignment that relies on the expectation of cost or mean excess of cost summation. This study develops a risk- and ambiguity-aware traffic … Read more
Negative Curvature Methods with High-Probability Complexity Guarantees for Stochastic Nonconvex Optimization
This paper develops negative curvature methods for continuous nonlinear unconstrained optimization in stochastic settings, in which function, gradient, and Hessian information is available only through probabilistic oracles, i.e., oracles that return approximations of a certain accuracy and reliability. We introduce conditions on these oracles and design a two-step framework that systematically combines gradient and negative … Read more