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Verification of Sequential Convex Programming for Parametric Non-convex Optimization
Rajiv Sambharya, Nikolai Matni, George Pappas
https://arxiv.org/abs/2511.10622 https://arxiv.org/pdf/2511.10622 https://arxiv.org/html/2511.10622
arXiv:2511.10622v1 Announce Type: new
Abstract: We introduce a verification framework to exactly verify the worst-case performance of sequential convex programming (SCP) algorithms for parametric non-convex optimization. The verification problem is formulated as an optimization problem that maximizes a performance metric (e.g., the suboptimality after a given number of iterations) over parameters constrained to be in a parameter set and iterate sequences consistent with the SCP update rules. Our framework is general, extending the notion of SCP to include both conventional variants such as trust-region, convex-concave, and prox-linear methods, and algorithms that combine convex subproblems with rounding steps, as in relaxing and rounding schemes. Unlike existing analyses that may only provide local guarantees under limited conditions, our framework delivers global worst-case guarantees--quantifying how well an SCP algorithm performs across all problem instances in the specified family. Applications in control, signal processing, and operations research demonstrate that our framework provides, for the first time, global worst-case guarantees for SCP algorithms in the parametric setting.
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Geometry of dyadic polygons I: the structure of dyadic triangles
A. Mu\'cka, A. Romanowska
https://arxiv.org/abs/2510.05467 https://arxiv.org/pdf/2510.…

Geometry of dyadic polygons I: the structure of dyadic triangles
Dyadic rationals are rationals whose denominator is a power of 2. A dyadic n-dimensional convex set is defined as the intersection with n-dimensional dyadic space of an n-dimensional real convex set. Such a dyadic convex set is said to be a dyadic n-dimensional polytope if the real convex set is a polytope whose vertices lie in the dyadic space. Dyadic convex sets are described as subalgebras of reducts of faithful affine spaces over the ring of dyadic numbers, or equivalently as commutative, e…

Volume functions and boundary data of 3-dimensional hyperbolic manifolds
Jean-Marc Schlenker
https://arxiv.org/abs/2510.05627 https://arxiv.org/pdf/2510.05…

Volume functions and boundary data of 3-dimensional hyperbolic manifolds
We review recent progress on two closely related sets of questions concerning convex co-compact hyperbolic manifolds, or convex domains in those manifolds, such as their convex core. The first set of questions is to what extent the hyperbolic metric on such a manifold is uniquely determined by either of two possible geometric data on their boundary. The second aspect is the ``volume'' associated to such a manifold, such as the renormalized volume of a convex co-compact hyperbolic manifold. The …

Polynomial convexity of $\bar\partial$-flat perturbations of totally real sets
Leandro Arosio, H{\aa}kan Samuelsson Kalm, Erlend F. Wold
https://arxiv.org/abs/2510.11943 https:/…

Polynomial convexity of $\bar\partial$-flat perturbations of totally real sets
We show that if $X$ is a totally real $d$-dimensional manifold attached to a polynomially convex compact set $K$ in $\mathbb{C}^n$, $d

Further analysis of Peeling Sequences
D\'aniel G\'abor Simon
https://arxiv.org/abs/2510.03832 https://arxiv.org/pdf/2510.03832

Further analysis of Peeling Sequences
Let $P\subset \mathbf{R}^2$ be a set of $n$ points in general position. A peeling sequence of $P$ is a list of its points, such that if we remove the points from $P$ in that order, we always remove the next point from the convex hull of the remainder of $P$. Using the methodology of Dumitrescu and Tóth \cite{Dumitrescu}, with more careful analysis, we improve the upper bound on the minimum number of peeling sequences for an $n$ point set in the plane from $\frac{12.29^n}{100}$ to $\frac{9.78^n…

The quasi-Assouad dimension of $(1,2t)$-Furstenberg sets in $\mathbb{R}^3$ is extremized by sticky sets
Sam Craig
https://arxiv.org/abs/2510.06462 https://…

The quasi-Assouad dimension of $(1,2t)$-Furstenberg sets in $\mathbb{R}^3$ is extremized by sticky sets
A $(1,2t)$-Furstenberg set in $\mathbb{R}^3$ is naturally defined as a set containing a union of unit line segments forming a $2t$-dimensional subset of the affine Grassmannian in $\mathbb{R}^3$ and satisfying a suitable variant of the Frostman Convex Wolff Axiom. Some of these sets have a multi-scale self-similarity property called stickiness. We investigate the extremizers of the quasi-Assouad dimension of $(1,2t)$-Furstenberg sets, a slightly stronger variant of the Assouad dimension. We pro…

Increasing Value of Information Implies Separable Utility
Michel de Lara (CERMICS)
https://arxiv.org/abs/2510.11102 https://arxiv.org/pdf/2510.11102…

Increasing Value of Information Implies Separable Utility
We consider decision-making under incomplete information about an unknown state of nature. Utility acts (that is, utility vectors indexed by states of nature) and beliefs (probability distributions over the states of nature) are naturally paired by bilinear duality, giving the expected utility. With this pairing, an expected utility maximizer (DM) is characterized by a continuous closed convex comprehensive set of utility acts (c-utility act set). We show that DM M values information more than …

Gradient regularity for widely degenerate parabolic equations
Michael Strunk
https://arxiv.org/abs/2510.07999 https://arxiv.org/pdf/2510.07999

Gradient regularity for widely degenerate parabolic equations
In this paper, we are interested in the regularity of weak solutions $u\colonΩ_T\to\mathbb{R}$ to parabolic equations of the type \begin{equation*} \partial_t u - \mathrm{div} \nabla \mathcal{F}(x,t,Du) = f\qquad\mbox{in $Ω_T$}, \end{equation*} where $\mathcal{F}$ is only elliptic for values of $Du$ outside a bounded and convex set $E\subset \mathbb{R}^n$ with the property that $0\in \mathrm{Int}{E}$. Here, $Ω_T :=Ω\times(0,T)\subset\mathbb{R}^{n+1}$ denotes a space-time cylinder taken ov…

Positive cones of $b$-divisor classes
Snehajit Misra, Nabanita Ray
https://arxiv.org/abs/2509.25948 https://arxiv.org/pdf/2509.25948

Positive cones of $b$-divisor classes
In this article, we define the notion of ample Cartier $b$-divisor classes by using the notion of Seshadri constants for Cartier $b$-divisor classes. In particular, we have shown that the set of all ample Cartier $b$-divisor classes forms a convex cone inside the nef cone of Cartier $b$-divisor classes. Furthermore, we have studied various properties of these Cartier ample $b$-divisor classes. We have also given an equivalent characterization of big Cartier $b$-divisor classes in terms of volum…

Correlated Perfect Equilibrium
Wanying Huang, J. Jude Kline, Priscilla Man
https://arxiv.org/abs/2510.07906 https://arxiv.org/pdf/2510.07906

Correlated Perfect Equilibrium
We propose a refinement of correlated equilibrium based on mediator errors, called correlated perfect equilibrium (CPE). In finite games, the set of CPE is nonempty and forms a finite union of convex sets. Like perfect equilibrium, a CPE never assigns positive probability to any weakly dominated strategy. We provide a dual representation of CPE and demonstrate how it differs from two existing refinements of correlated equilibrium--acceptable correlated equilibrium (Myerson, 1986) and perfect di…

Almost toric fibrations on symplectic blow ups
Pranav Chakravarthy, Yoel Groman
https://arxiv.org/abs/2510.00994 https://arxiv.org/pdf/2510.00994

Almost toric fibrations on symplectic blow ups
Given a symplectic 4-manifold with an almost toric fibration and a symplectic ball embedding whose image under the moment map is contained in an affine convex set R, we produce a symplectomorphism between the almost toric blow-up and the symplectic blow-up which is the identity on the pre-image of the complement of R. Furthermore, under a compatibility condition of the ball embedding with the boundary divisor, we show that the symplectomorphism can be chosen to preserve the induced symplectic l…

Measuring dissimilarity between convex cones by means of max-min angles
Welington de Oliveira, Valentina Sessa, David Sossa
https://arxiv.org/abs/2511.10483 https://arxiv.org/pdf/2511.10483 https://arxiv.org/html/2511.10483
arXiv:2511.10483v1 Announce Type: new
Abstract: This work introduces a novel dissimilarity measure between two convex cones, based on the max-min angle between them. We demonstrate that this measure is closely related to the Pompeiu-Hausdorff distance, a well-established metric for comparing compact sets. Furthermore, we examine cone configurations where the measure admits simplified or analytic forms. For the specific case of polyhedral cones, a nonconvex cutting-plane method is deployed to compute, at least approximately, the measure between them. Our approach builds on a tailored version of Kelley's cutting-plane algorithm, which involves solving a challenging master program per iteration. When this master program is solved locally, our method yields an angle that satisfies certain necessary optimality conditions of the underlying nonconvex optimization problem yielding the dissimilarity measure between the cones. As an application of the proposed mathematical and algorithmic framework, we address the image-set classification task under limited data conditions, a task that falls within the scope of the \emph{Few-Shot Learning} paradigm. In this context, image sets belonging to the same class are modeled as polyhedral cones, and our dissimilarity measure proves useful for understanding whether two image sets belong to the same class.
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On rigid $q$-plurisubharmonic functions and $q$-pseudoconvex tube domains in $\mathbb{C}^n$
Thomas Pawlaschyk
https://arxiv.org/abs/2510.05009 https://arxi…

On rigid $q$-plurisubharmonic functions and $q$-pseudoconvex tube domains in $\mathbb{C}^n$
In the spirit of Lelong and Bochner, we show that an upper semi-continuous function defined on a open tube set $Ω=ω+ i\mathbb{R}^n$ in $\mathbb{C}^n$, where $ω$ is an open set in $\mathbb{R}^n$, and which is invariant in its imaginary part, is $q$-plurisubharmonic on $Ω$ (in the sense of Hunt and Murray) if and only if it is real $q$-convex on $ω$, i.e., it admits the local maximum property with respect to affine linear functions on real $(q+1)$-dimensional affine subspaces. From this, we …

Error estimates for finite-dimensional approximations of Hamilton-Jacobi-Bellman equations on the Wasserstein space
Samuel Daudin, Joe Jackson, Benjamin Seeger
https://arxiv.org/abs/2510.02652

Error estimates for finite-dimensional approximations of Hamilton-Jacobi-Bellman equations on the Wasserstein space
In this paper, we study a Hamilton-Jacobi-Bellman (HJB) equation set on the Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$, with a second order term arising from a purely common noise. We do not assume that the Hamiltonian is convex in the momentum variable, which means that we cannot rely on representation formulas coming from mean field control. In this setting, Gangbo, Mayorga, and Święch showed via viscosity solutions methods that the HJB equation on $\mathcal{P}_2(\mathbb{R}^d)$ can be …

Replaced article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- A robust BFGS algorithm for unconstrained nonlinear optimization problems
Yaguang Yang
https://arxiv.org/abs/1212.5929
- Quantum computing and the stable set problem
Alja\v{z} Krpan, Janez Povh, Dunja Pucher
https://arxiv.org/abs/2405.12845 https://mastoxiv.page/@arXiv_mathOC_bot/112483516437815686
- Mean Field Game with Reflected Jump Diffusion Dynamics: A Linear Programming Approach
Zongxia Liang, Xiang Yu, Keyu Zhang
https://arxiv.org/abs/2508.20388 https://mastoxiv.page/@arXiv_mathOC_bot/115111048711698998
- Differential Dynamic Programming for the Optimal Control Problem with an Ellipsoidal Target Set a...
Sungjun Eom, Gyunghoon Park
https://arxiv.org/abs/2509.07546 https://mastoxiv.page/@arXiv_mathOC_bot/115179281556444440
- On the Moreau envelope properties of weakly convex functions
Marien Renaud, Arthur Leclaire, Nicolas Papadakis
https://arxiv.org/abs/2509.13960 https://mastoxiv.page/@arXiv_mathOC_bot/115224514482363803
- Automated algorithm design via Nevanlinna-Pick interpolation
Ibrahim K. Ozaslan, Tryphon T. Georgiou, Mihailo R. Jovanovic
https://arxiv.org/abs/2509.21416 https://mastoxiv.page/@arXiv_mathOC_bot/115286533597711930
- Optimal Control of a Bioeconomic Crop-Energy System with Energy Reinvestment
Othman Cherkaoui Dekkaki
https://arxiv.org/abs/2510.11381 https://mastoxiv.page/@arXiv_mathOC_bot/115372322896073250
- Point Convergence Analysis of the Accelerated Gradient Method for Multiobjective Optimization: Co...
Yingdong Yin
https://arxiv.org/abs/2510.26382 https://mastoxiv.page/@arXiv_mathOC_bot/115468018035252078
- History-Aware Adaptive High-Order Tensor Regularization
Chang He, Bo Jiang, Yuntian Jiang, Chuwen Zhang, Shuzhong Zhang
https://arxiv.org/abs/2511.05788
- Equivalence of entropy solutions and gradient flows for pressureless 1D Euler systems
Jos\'e Antonio Carrillo, Sondre Tesdal Galtung
https://arxiv.org/abs/2312.04932 https://mastoxiv.page/@arXiv_mathAP_bot/111560077272113052
- Kernel Modelling of Fading Memory Systems
Yongkang Huo, Thomas Chaffey, Rodolphe Sepulchre
https://arxiv.org/abs/2403.11945 https://mastoxiv.page/@arXiv_eessSY_bot/112121123836064435
- The Maximum Theoretical Ground Speed of the Wheeled Vehicle
Altay Zhakatayev, Mukatai Nemerebayev
https://arxiv.org/abs/2502.15341 https://mastoxiv.page/@arXiv_physicsclassph_bot/114057765769441123
- Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavity
Giacomo Greco, Luca Tamanini
https://arxiv.org/abs/2504.11133 https://mastoxiv.page/@arXiv_mathPR_bot/114346453424694503
- Optimizing the ground state energy of the three-dimensional magnetic Dirichlet Laplacian with con...
Matthias Baur
https://arxiv.org/abs/2504.21597 https://mastoxiv.page/@arXiv_mathph_bot/114431404740241516
- A localized consensus-based sampling algorithm
Arne Bouillon, Alexander Bodard, Panagiotis Patrinos, Dirk Nuyens, Giovanni Samaey
https://arxiv.org/abs/2505.24861 https://mastoxiv.page/@arXiv_mathNA_bot/114612580684567066
- A Novel Sliced Fused Gromov-Wasserstein Distance
Moritz Piening, Robert Beinert
https://arxiv.org/abs/2508.02364 https://mastoxiv.page/@arXiv_csLG_bot/114976243138728278
- Minimal Regret Walras Equilibria for Combinatorial Markets via Duality, Integrality, and Sensitiv...
Alo\"is Duguet, Tobias Harks, Martin Schmidt, Julian Schwarz
https://arxiv.org/abs/2511.09021 https://mastoxiv.page/@arXiv_csGT_bot/115541243299714775
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The Non-Attainment Phenomenon in Robust SOCPs
Vinh Nguyen
https://arxiv.org/abs/2510.00318 https://arxiv.org/pdf/2510.00318

The Non-Attainment Phenomenon in Robust SOCPs
A fundamental theorem of linear programming states that a feasible linear program is solvable if and only if its objective function is copositive with respect to the recession cone of its feasible set. This paper demonstrates that this crucial guarantee does not extend to Second-Order Cone Programs (SOCPs), a workhorse model in robust and convex optimization. We construct and analyze a rigorous counterexample derived from a robust linear optimization problem with ellipsoidal uncertainty. The re…