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We approach the problem of finding obstructions to curvature distinguished Riemannian metrics by considering Lorentzian metrics to which they are dual in a suitable sense. Obstructions to the latter then yield obstructions to the former.…
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…
The aim of this work is to study, from an intrinsic and geometric point of view, second-order constrained variational problems on Lie algebroids, that is, optimization problems defined by a cost functional which depends on higher-order…
The aim of this paper is to adapt the general multitime maximum principle to a Riemannian setting. More precisely, we intend to study geometric optimal control problems constrained by the metric compatibility evolution PDE system; the…
In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in…
This paper studies approximate solutions of a linear fractional vector optimization problem without requiring boundedness of the constraint set. We establish necessary and sufficient conditions for approximating weakly efficient points of…
This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the…
We prove existence of radially symmetric solutions and validity of Euler-Lagrange necessary conditions for a class of variational problems such that neither direct methods nor indirect methods of Calculus of Variations apply. We obtain…
This paper introduces the use of tailored variational forms for variational quantum eigensolver that have properties of representing certain constraints on the search domain of a linear constrained quadratic binary optimization problem…
When dealing with general Lipschitzian optimization problems, there are many problem classes where even weak constraint qualifications fail at local minimizers. In contrast to a constraint qualification, a problem qualification does not…
We consider the optimization problem with a generally quadratic matrix constraint of the form $X^TAX = J$, where $A$ is a given nonsingular, symmetric $n\times n$ matrix and $J$ is a given $k\times k$ symmetric matrix, with $k\leq n$,…
We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$),…
By using variational techniques we provide new existence results for Yamabe-type equations with subcritical perturbations set on a compact $d$-dimensional ($d\geq 3$) Riemannian manifold without boundary. As a direct consequence of our main…
Many modern machine learning applications - from online principal component analysis to covariance matrix identification and dictionary learning - can be formulated as minimization problems on Riemannian manifolds, and are typically solved…
In this paper, we introduce a general framework for analyzing the numerical conditioning of minimal problems in multiple view geometry, using tools from computational algebra and Riemannian geometry. Special motivation comes from the fact…
Optimization problems over compact Lie groups have been extensively studied due to their broad applications in linear programming and optimal control. This paper analyzes least square problems over a noncompact Lie group, the symplectic…
We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a penalised and smoothed problem and studying convergence of the…
We study the reduction of degrees of freedom for the equations that determine necessary optimality conditions for extrema in an optimal control problem for a multiagent system by exploiting the physical symmetries of agents, where the…
Motivated by optimal control problems and differential games for functional differential equations of retarded type, the paper deals with a Cauchy problem for a path-dependent Hamilton--Jacobi equation with a right-end boundary condition.…
Approximate necessary optimality conditions in terms of Fr\'echet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective function are established with the aid of Ekeland's…