We study the lift-and-project relaxations of the stable set polytope of graphs generated by \( \text{LS}_+ \), the SDP lift-and-project operator devised by Lovász and Schrijver. In particular, we focus on searching for \( \ell \)-minimal graphs, which are graphs on $3\ell$ vertices whose stable set polytope has rank \( \ell \) with respect to … Read more
We study weighted, capacitated cost-sharing games on parallel-link networks, also known as bin packing games. We focus on an integer-splittable variant in which items of varying sizes can be divided into integer units and assigned to bins with heterogeneous capacities and costs. Although this setting has practical relevance, it remains largely unexplored in the context … Read more
Generalized Nash equilibrium problems with mixed-integer variables form an important class of games in which each player solves a mixed-integer optimization problem with respect to her own variables and the strategy space of each player depends on the strategies chosen by the rival players. In this work, we introduce a branch-and-cut algorithm to compute exact … Read more
The widespread existence of various uncertainties makes the inherently complex refinery production scheduling problem even more challenging. To address this issue, this paper proposes a viable systematic data-driven multistage scheduling optimization framework and develops a corresponding structured modeling methodology. Under this paradigm, unit-level advanced control and plant-level intelligent scheduling are coordinated to jointly deal with … Read more
This paper establishes the theoretical foundations of the online scaled gradient methods (OSGM), a framework that utilizes online learning to adapt stepsizes and provably accelerate first-order methods. OSGM quantifies the effectiveness of a stepsize by a feedback function motivated from a convergence measure and uses the feedback to adjust the stepsize through an online learning … Read more
We present a stochastic inexact Gauss-Newton method for the solution of nonlinear least-squares. To reduce the computational cost with respect to the classical method, at each iteration the proposed algorithm approximately minimizes the local model on a random subspace. The dimension of the subspace varies along the iterations, and two strategies are considered for its … Read more
The proximal alternating predictor-corrector (PAPC) method is a widely used first-order algorithm for solving convex-concave saddle-point problems involving both smooth and nonsmooth components. Unlike the primal-dual hybrid gradient (PDHG) method, which incorporates an extrapolation step with parameter $\theta \in (0,1]$ to improve convergence, the existing convergence analysis of PAPC has been limited to the case … Read more
This paper proposes a novel approach for solving linear programs. We reformulate a primal-dual linear program as an unconstrained minimization of a convex and twice continuously differentiable merit function. When the optimal set of the primal-dual pair is nonempty, its optimal set is equal to the optimal set of the proposed merit function. Minimizing this … Read more
In this paper, we propose a framework based on the Retrospective Approximation (RA) paradigm to solve optimization problems with a stochastic objective function and general nonlinear deterministic constraints. This framework sequentially constructs increasingly accurate approximations of the true problems which are solved to a specified accuracy via a deterministic solver, thereby decoupling the uncertainty from … Read more
Real world problems often require complex modeling and computation efforts to be effectively addressed. Relying solely on data-driven approaches without integrating physics-based models can result in limited predictive capabilities. Even advanced techniques such as deep learning may be impractical for decision-makers due to the lack of data and challenges in justifying and explaining results. In … Read more