We study order acceptance dynamics in same-day delivery systems by formulating the Dynamic Dispatch Waves Problem with Immediate Acceptance, which models integrated request management and order distribution for dynamically arriving requests. When a delivery request arrives, a decision is made immediately to accept (offer service) or reject (with a penalty). Accepted requests are not available … Read more
We analyze an inner approximation scheme for probability maximization. The approach was proposed in Fabian, Csizmas, Drenyovszki, Van Ackooij, Vajnai, Kovacs, Szantai (2018) Probability maximization by inner approximation, Acta Polytechnica Hungarica 15:105-125, as an analogue of a classic dual approach in the handling of probabilistic constraints. Even a basic implementation of the maximization scheme proved … Read more
This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie’s and Guignard’s kink qualification and … Read more
Historically, scalability has been a major challenge to the successful application of semidefinite programming in fields such as machine learning, control, and robotics. In this paper, we survey recent approaches for addressing this challenge including (i) approaches for exploiting structure (e.g., sparsity and symmetry) in a problem, (ii) approaches that produce low-rank approximate solutions to … Read more
In this paper, a reformulation that was proposed for a knapsack problem has been extended to single and bi-objective linear integer programs. A further reformulation by adding an upper bound constraint for a knapsack problem is also proposed and extended to the bi-objective case. These reformulations significantly reduce the number of branch and bound iterations … Read more
The concepts of risk-aversion, chance-constrained optimization, and robust optimization have developed significantly over the last decade. Statistical learning community has also witnessed a rapid theoretical and applied growth by relying on these concepts. A modeling framework, called distributionally robust optimization (DRO), has recently received significant attention in both the operations research and statistical learning communities. … Read more
This paper is on multiobjective bilevel optimization, i.e. on bilevel optimization problems with multiple objectives on the lower or on the upper level, or even on both levels. We give an overview on the major optimality notions used in multiobjective optimization. We provide characterization results for the set of optimal solutions of multiobjective optimization problems … Read more
In semidefinite programming a proposed optimal solution may be quite poor in spite of having sufficiently small residual in the optimality conditions. This issue may be framed in terms of the discrepancy between forward error (the unmeasurable `true error’) and backward error (the measurable violation of optimality conditions). In his seminal work, Sturm provided an … Read more
Linear energy system models are often a crucial component of system design and operations, as well as energy policy consulting. Such models can lead to large-scale linear programs, which can be intractable even for state-of-the-art commercial solvers—already the available memory on a desktop machine might not be sufficient. Against this backdrop, this article introduces an … Read more
Stochastic convex optimization problems with expectation constraints (SOECs) are encountered in statistics and machine learning, business, and engineering. In data-rich environments, the SOEC objective and constraints contain expectations defined with respect to large datasets. Therefore, efficient algorithms for solving such SOECs need to limit the fraction of data points that they use, which we refer … Read more