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The goal of this work is to propose a new type of constraint for linear programs: inequalities having infinite, finite, and infinitesimal values in the right-hand side. Because of the nature of such constraints, the feasible region polyhedron ...

This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in continuous time. It is known that these problems are related to certain infinite-dimensional linear programming ...

• We address single machine scheduling problem with flexible/variable maintenance.
• We introduce three new MILP models.
• We present a novel heuristic algorithm configured into three distinct variants.
• We compare several heuristic ...

Inspired by a real-world maintenance/job scheduling issue coming from the semiconductor industry, the present paper proposes a new heuristic algorithm structure for the single machine scheduling T-problem with flexible and variable maintenance, ...

Many complex decision-making scenarios encountered in the real-world, including energy systems and infrastructure planning, can be formulated as constrained optimization problems. Solutions for these problems are often obtained using white-box ...

• We introduce a problem solving paradigm to study explanations for optimization.
• We utilize an exploration and a sequential decision-making version of the task.
• We derive formal strategies from explanations, verbal reports, and ...

Linear Programming is one of the most common methods for finding optimal solutions to complex problems. Despite its extensive use, solutions are not usually accompanied by explanations, especially explanations for non-experts. Our new tool ...

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• We generalized the dominance relation for variables to weak dominance and can thereby explain more cases without changing the optimal solution.
• Our tool SimplifEx produces a graph with edges showing dominance relations between ...

We study the restricted inverse optimal value problem on minimum spanning tree under weighted l 1 norm. In a connected edge-weighted network G(V,E,w), we are given a spanning tree T 0, a cost vector c and a value K. We aim to obtain a new weight ...

We analyze restarted PDHG on totally unimodular linear programs. In particular, we show that restarted PDHG finds an ϵ-optimal solution in O ( H m 1 2.5 nnz ( A ) log ⁡ ( H m 2 / ϵ ) ) matrix-vector multiplies where m 1 is the number of ...

Given a set of full-rank matrices A 1 , A 2 , … , A r ∈ R p × n, this brief paper proposes a method based on linear feasibility tests to determine whether a convex combination A ( α ) = ∑ i = 1 r α i A i, with α = [ α 1 α 2 ⋯ α r ] T in the unit ...

A cofactor representation of an ideal element, that is, a representation in terms of the generators, can be considered as a certificate for ideal membership. Such a representation is typically not unique, and some can be a lot more complicated ...

Multi-Protocol Label Switching (MPLS) sets up a connecting tunnel for each origin–destination pair of traffic demands to send data packets over Internet Protocol (IP) networks. We should assign each tunnel to one of the available candidate paths ...

Crystals-Kyber, a key encapsulation mechanism (KEM) whose security is based on the Module-LWE problem, has recently been selected by NIST as part of its post-quantum cryptography initiative. At ASIACRYPT 2021, Qin et al. gave a method to evaluate ...

We study a general optimization problem with an uncertain linear objective. We address the uncertainty using two models: belief functions and, more generally, capacities. In the former model, we use the generalized minimax regret criterion ...

With the rapid development and wide application of neural networks in various domains including safety-critical systems, it is more and more important to investigate formal methods to provide strict guarantees on their behavior. As formal ...

The Chinese postman problem (CPP) is a widely recognized combinatorial optimization problem with numerous real-world applications. Modeling such real-world applications often involves considering uncertain variables. Robust optimization is one of ...$$

Given samples of a real or complex-valued function on a set of distinct nodes, the traditional linear Chebyshev approximation is to compute the minimax approximation on a prescribed linear functional space. Lawson’s iteration is a classical and ...${}_{}$${}_{\mathrm{}}$

This paper is intended as a companion to [12] and focuses on the numerical implementations of the method in the context of insurance problems with mixed controls: reinsurance acting as continuous control, and capital injection and dividend ...

• We provide a validation of the Dual Linear Programming algorithm by showcasing its performance on two benchmarks.
• With a relatively modest order of moments (4), the relative errors are of at most 3%.
• Leveraging this algorithm ...

We explore the complexity of nucleolus computation in b-matching games on bipartite graphs. We show that computing the nucleolus of a simple b-matching game is NP-hard when b ≡ 3 even on bipartite graphs of maximum degree 7. We complement this ...

• We explore the complexity of nucleolus computation in b-matching games on bipartite graphs.
• Computing the nucleolus of a simple b-matching game is NP-hard when b = 3 even on bipartite graphs of maximum degree 7.
• We complement this ...

Designing large-scale control systems to satisfy complex specifications is hard in practice, as most formal methods are limited to systems of modest size. Contract theory has been proposed as a modular alternative, in which specifications are ...

This paper studies constrained Markov decision processes under the total expected discounted cost optimality criterion, with a state-action dependent discount factor that may take any value between zero and one. Both the state and the action space ...

It was previously shown by the authors that a directed graph on a linearly ordered set of edges (ordered graph) with adjacent unique source and sink (bipolar digraph) has a unique fully optimal spanning tree, that satisfies a simple criterion on ...