相关论文: Canonical Duality Theory and Algorithm for Solving…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…
In this paper, the problem of low-latency communication and computation resource allocation for digital twin (DT) over wireless networks is investigated. In the considered model, multiple physical devices in the physical network (PN) needs…
Canonical Polyadic Decomposition (CPD) of a third-order tensor is decomposition in a minimal number of rank-$1$ tensors. We call an algorithm algebraic if it is guaranteed to find the decomposition when it is exact and if it only relies on…
The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to…
Canonical correlation analysis is a family of multivariate statistical methods for the analysis of paired sets of variables. Since its proposition, canonical correlation analysis has for instance been extended to extract relations between…
We consider the standard optimistic bilevel optimization problem, in particular upper- and lower-level constraints can be coupled. By means of the lower-level value function, the problem is transformed into a single-level optimization…
The unbounded knapsack problem with bounded weights is a variant of the well-studied variant of the traditional binary knapsack problem; key changes being the relaxation of the binary constraint and allowing the unit weights of each item to…
Causal Dynamical Triangulations (CDT) is a methodology to define and compute the gravitational path integral, whose aim is a fully fledged nonperturbative quantum field theory of gravity and spacetime. Analogous to lattice formulations of…
In this paper, we focus on knapsack cones, a specific type of simplicial cones that arise naturally in the context of the knapsack problem $x_1 a_1 + \cdots + x_n a_n = a_0$. We present a novel combinatorial decomposition for these cones,…
Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of…
Quantum algorithms for topological data analysis (TDA) seem to provide an exponential advantage over the best classical approach while remaining immune to dequantization procedures and the data-loading problem. In this paper, we give…
Consider the joint beamforming and quantization problem in the cooperative cellular network, where multiple relay-like base stations (BSs) connected to the central processor (CP) via rate-limited fronthaul links cooperatively serve the…
Canonical correlation analysis (CCA) is a multivariate statistical technique for finding the linear relationship between two sets of variables. The kernel generalization of CCA named kernel CCA has been proposed to find nonlinear relations…
The formalism of causal dynamical triangulations (CDT) provides us with a non-perturbatively defined model of quantum gravity, where the sum over histories includes only causal space-time histories. Path integrals of CDT and their continuum…
We suggest a hybrid quantum-classical routine for the NP-hard Electric Vehicle Fleet Charging and Allocation Problem. The original formulation is a Mixed Integer Linear Program with continuous variables and inequality constraints. To…
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…
Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…
This paper focuses on developing effective algorithms for solving bilevel program. The most popular approach is to replace the lower-level problem by its Karush-Kuhn-Tucker conditions to generate a mathematical program with complementarity…
Learning representations of two views of data such that the resulting representations are highly linearly correlated is appealing in machine learning. In this paper, we present a canonical correlation guided learning framework, which allows…
A new approach to linear programming duality is proposed which relies on quadratic penalization, so that the relation between solutions to the penalized primal and dual problems becomes affine. This yields a new proof of Levin's duality…