相关论文: Canonical Duality Theory and Algorithm for Solving…
Canonical Polyadic (or CANDECOMP/PARAFAC, CP) decompositions (CPD) are widely applied to analyze high order tensors. Existing CPD methods use alternating least square (ALS) iterations and hence need to unfold tensors to each of the $N$…
In this paper, we formulate the Canonical Correlation Analysis (CCA) problem on matrix manifolds. This framework provides a natural way for dealing with matrix constraints and tools for building efficient algorithms even in an adaptive…
Critical node problems involve identifying a subset of critical nodes from an undirected graph whose removal results in optimizing a pre-defined measure over the residual graph. As useful models for a variety of practical applications,…
Digital twins are emerging in many industries, typically consisting of simulation models and data associated with a specific physical system. One of the main reasons for developing a digital twin, is to enable the simulation of possible…
Industrial Control Systems (ICS) in water distribution and treatment face cyber-physical attacks exploiting network and physical vulnerabilities. Current water system anomaly detection methods rely on correlations, yielding high false…
A double partition problem asks for a number of nonnegative integer solutions to a system of two linear Diophantine equations with integer coefficients. Artur Cayley suggested a reduction of a double partition to a sum of scalar partitions…
A powerful strategy to treat quantum field theories beyond perturbation theory is by putting them on a lattice. However, the dynamical and symmetry structure of general relativity have for a long time stood in the way of a well-defined…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
One revisits the standard saddle-point method based on conjugate duality for solving convex minimization problems. Our aim is to reduce or remove unnecessary topological restrictions on the constraint set. Dual equalities and…
The bin packing problem, a classical NP-hard combinatorial optimization challenge, has emerged as a promising candidate for quantum computing applications. In this work, we address the one-dimensional bin packing problem (1dBPP) using a…
For a primal-dual pair of conic linear problems that are described by convex cones $S\subset X$, $T\subset Y$, bilinear symmetric objective functions $\langle\cdot,\cdot\rangle_X$, $\langle\cdot,\cdot\rangle_Y$ and a linear operator…
In this paper we consider a general, challenging distributed optimization set-up arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…
The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence. Against this background, we study the expressive power of neural networks through…
Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…
Lin, Chan (High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting, 2024) enforces a cell entropy inequality for nodal discontinuous Galerkin methods by combining flux corrected transport…
The complementarity knapsack problem (CKP) is a knapsack problem with real-valued variables and complementarity conditions between pairs of its variables. We extend the polyhedral studies of De Farias et al. for CKP, by proposing three new…
In convex optimization, duality theory can sometimes lead to simpler solution methods than those resulting from direct primal analysis. In this paper, this principle is applied to a class of composite variational problems arising in…
We study a class of integer bilevel programs with second-order cone constraints at the upper-level and a convex-quadratic objective function and linear constraints at the lower-level. We develop disjunctive cuts (DCs) to separate…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…