Related papers: Trust-region and $p$-regularized subproblems: loca…
The $p$-regularized subproblem (p-RS) is a regularisation technique in computing a Newton-like step for unconstrained optimization, which globally minimizes a local quadratic approximation of the objective function while incorporating with…
Generalized trust-region subproblem (GT) is a nonconvex quadratic optimization with a single quadratic constraint. It reduces to the classical trust-region subproblem (T) if the constraint set is a Euclidean ball. (GT) is polynomially…
We study large scale extended trust region subproblems (eTRS) i.e., the minimization of a general quadratic function subject to a norm constraint, known as the trust region subproblem (TRS) but with an additional linear inequality…
In this paper, we study the local-nonglobal minimizers of the Generalized Trust-Region subproblem $(GTR)$ and its Equality-constrained version $(GTRE)$. Firstly, the equivalence is established between the local-nonglobal minimizers of both…
We consider minimization of indefinite quadratics with either trust-region (norm) constraints or cubic regularization. Despite the nonconvexity of these problems we prove that, under mild assumptions, gradient descent converges to their…
We consider the nonconvex minimization problem, with quartic objective function, that arises in the exact recovery of a configuration matrix $P\in \R^{nd}$ of $n$ points when a Euclidean distance matrix, \EDMp, is given with embedding…
In this note, we focus on smooth nonconvex optimization problems that obey: (1) all local minimizers are also global; and (2) around any saddle point or local maximizer, the objective has a negative directional curvature. Concrete…
A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…
We consider a nonlocal isoperimetric problem defined in the whole space $\R^N$, whose nonlocal part is given by a Riesz potential with exponent $\alpha\in(0, N-1)$. We show that critical configurations with positive second variation are…
In this article, we develop a trust-region technique to find critical points of unconstrained set optimization problems with the objective set-valued map defined by finitely many twice continuously differentiable functions. The technique is…
We have an $\m\x\n$ real-valued arbitrary matrix $A$ (e.g. a dictionary) with $\m<\n$ and data $d$ describing the sought-after object with the help of $A$. This work provides an in-depth analysis of the (local and global) minimizers of an…
In this paper, we analyze some theoretical properties of the problem of minimizing a quadratic function with a cubic regularization term, arising in many methods for unconstrained and constrained optimization that have been proposed in the…
In this article we study eigenvalues and minimizers of a fractional non-standard growth problem. We prove several properties on this quantities and their corresponding eigenfunctions.
This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimizers for a broad class of…
We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational inequalities of the second kind. Under suitable assumptions on…
This paper is devoted to the study of tilt stability of local minimizers, which plays an important role in both theoretical and numerical aspects of optimization. This notion has been comprehensively investigated in the unconstrained…
We prove a full Harnack inequality for local minimizers, as well as weak solutions to nonlocal problems with non-standard growth. The main auxiliary results are local boundedness and a weak Harnack inequality for functions in a…
Tilt stability plays a pivotal role in understanding how local solutions of an optimization problem respond to small, targeted perturbations of the objective. Although quadratic bundles are a powerful tool for capturing second-order…
We study unconstrained control of a two-level quantum system and analyse critical points of the objective functional which represents quantum average of system observable at some final time $T$. In Proc. Steklov Inst. Math. 285, 233-240…
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…