相关论文: Strong Duality for Generalized Trust Region Subpro…

We prove a duality theorem for graded algebras over a field that implies several known duality results : graded local duality, versions of Serre duality for local cohomology and of Suzuki duality for generalized local cohomology, and…

We are concerned with finding the set $I_{\succeq}(A,B)$ of real values $\mu$ such that the matrix pencil $A+\mu B$ is positive semidefinite. If $A, B$ are not simultaneously diagonalizable via congruence (SDC), $I_{\succeq}(A,B)$ either is…

We evaluate the superconformal index of 4d $\mathcal{N}=4$ SYM with gauge algebra $so(2N_c+1)$ in the Cardy-like limit. We then study the relation with the results obtained for the S-dual $usp(2N_c)$, discussing the fate of S-duality in…

In this paper, we present sufficient conditions ensuring that the sum of the image of quadratic functions and the nonnegative orthant is convex. The hidden convexity of the trust-region problem with linear inequality constraints is…

We develop a methodology for closing duality gap and guaranteeing strong duality in infinite convex optimization. Specifically, we examine two new Lagrangian-type dual formulations involving infinitely many dual variables and infinite sums…

Cosmological perturbation equations derived from low-energy effective actions are shown to be invariant under a duality transformation reminiscent of electric-magnetic, strong-weak coupling, S-duality. A manifestly duality-invariant…

We define a duality operation connecting closure operations, interior operations, and test ideals, and describe how the duality acts on common constructions such as trace, torsion, tight and integral closures, and divisible submodules. This…

We generalize Blumberg-Mandell's K-theoretic Poitou-Tate duality to arithmetic schemes of arbitrary dimension, smooth and proper over S-integers. As in our earlier papers on the subject, we discuss how to model the compactly supported side…

We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSI's. The recently introduced duality on SSI's is given an effective conceptual and computational setting. We study strongly…

We investigate the `local consistency implies global consistency' principle of strict width among structures within the scope of the Bodirsky-Pinsker dichotomy conjecture for infinite-domain Constraint Satisfaction Problems (CSPs). Our main…

Let $X_1, \ldots, X_n$ be some i.i.d. observations from a heavy tailed distribution $F$, i.e. such that the common distribution of the excesses over a high threshold $u_n$ can be approximated by a Generalized Pareto Distribution…

We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log…

We propose a duality in the relative Langlands program. This duality pairs a Hamiltonian space for a group $G$ with a Hamiltonian space under its dual group $\check{G}$, and recovers at a numerical level the relationship between a period on…

We prove a duality theorem the computation of certain Bellman functions is usually based on. As a byproduct, we obtain sharp results about the norms of monotonic rearrangements. The main novelty of our approach is a special class of…

We present an announcement of some recent results concerning well-posedness of the Poisson-Dirichlet problem with boundary data in Besov spaces with fractional smoothness. This is a far-reaching generalization as previously known theorems…

The work studies the problem of decentralized constrained POMDPs in a team-setting where multiple nonstrategic agents have asymmetric information. Using an extension of Sion's Minimax theorem for functions with positive infinity and results…

We show that sparsity constrained optimization problems over low dimensional spaces tend to have a small duality gap. We use the Shapley-Folkman theorem to derive both data-driven bounds on the duality gap, and an efficient primalization…

We consider the convex bilevel optimization problem, also known as simple bilevel programming. There are two challenges in solving convex bilevel optimization problems. Firstly, strong duality is not guaranteed due to the lack of Slater…

Recent advances in statistics introduced versions of the central limit theorem for high-dimensional vectors, allowing for the construction of confidence regions for high-dimensional parameters. In this note, $s$-sparsely convex…

The Trust Region Subproblem is a fundamental optimization problem that takes a pivotal role in Trust Region Methods. However, the problem, and variants of it, also arise in quite a few other applications. In this article, we present a…