Motivated by the need for reliable traffic management under fluctuating travel demand, we study the problem of determining the worst-case congestion in a multi-commodity traffic network subject to demand uncertainty. To this end, we stress-test a given network by identifying demand realizations and corresponding travelers’ route choices that maximize congestion. The users of the traffic … Read more
We develop two penalty based difference of convex (DC) algorithms for solving chance constrained programs. First, leveraging a rank-based DC decomposition of the chance constraint, we propose a proximal penalty based DC algorithm in the primal space that does not require a feasible initialization. Second, to improve numerical stability in the general nonlinear settings, we … Read more
For mixed-integer linear programming and linear programming it is well known that symmetries can have a negative impact on the performance of branch-and-bound and linear optimization algorithms. A common strategy to handle symmetries in linear programs is to reduce the dimension of the linear program by aggregating symmetric variables and solving a linear program of … Read more
We develop a successive, proximal difference-of-convex (DC) function penalty method for solving DC programs with DC constraints. The proposed approach relies on a DC penalty function that measures the violation of constraints and leads to a penalty reformulation sharing the same solution set as the original problem. The resulting penalty problem is a DC program … Read more
Inverse optimization problems are bilevel optimization problems in which the leader modifies the follower’s objective such that a prescribed feasible solution becomes an optimal solution of the follower. They capture hierarchical decision-making problems like parameter estimation tasks or situations where a planner wants to steer an agent’s choice. In this work, we study integral inverse … Read more
We study generalized variational inequalities with a three-level hierarchical structure. This setting extends nested GVI models beyond the bilevel case, for which $\mathcal{O}(\delta^{-4})$ complexity bounds are known for any prescribed positive tolerance $\delta$, to a fully three-level hierarchical structure. We analyze a projected averaged subgradient method combined with a Tikhonov-like regularization scheme. Under compactness, maximal … Read more
In this work, we study stationarity conditions and constraint qualifications (CQs) tailored to Generalized Nash Equilibrium Problems (GNEPs) and analyze their relationships and implications for the global convergence of algorithms. We recall that GNEPs generalize Nash Equilibrium Problems (NEPs) in that the feasible strategy set of each player depends on the strategies chosen by the … Read more
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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
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