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It has recently been shown (Burer, Math. Program Ser. A 120:479-495, 2009) that a large class of NP-hard nonconvex quadratic programming problems can be modeled as so called completely positive programming problems, which are convex but…

Optimization and Control · Mathematics 2012-11-26 Chuan-Hao Guo , Yan-Qin Bai , Li-Ping Tang

In this paper, we study second-order necessary and sufficient optimality conditions of Karush--Kuhn--Tucker-type for locally optimal solutions in the sense of Pareto to a class of multi-objective optimal control problems with mixed…

Optimization and Control · Mathematics 2017-12-29 Bui Trong Kien , Nguyen Van Tuyen , Jen-Chih Yao

The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…

Optimization and Control · Mathematics 2011-10-21 B. S. Mordukhovich , R. T. Rockafellar

Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of…

Optimization and Control · Mathematics 2018-11-20 Coralia Cartis , Nicholas I. M. Gould , Philippe L. Toint

In the present paper, we focus on the vector optimization problems with inequality constraints, where objective functions and constrained functions are Fr\'echet differentiable, and whose gradient mapping is locally Lipschitz on an open…

Optimization and Control · Mathematics 2017-05-08 Nguyen Quang Huy , Do Sang Kim , Nguyen Van Tuyen

The details of second-order partial derivatives of rigid-body Inverse/Forward dynamics are provided. Several properties and identities using Spatial Vector Algebra are listed, along with their detailed derivations. The expressions build…

Robotics · Computer Science 2023-08-01 Shubham Singh , Ryan P. Russell , Patrick M. Wensing

This paper pursues a two-fold goal. Firstly, we aim to derive novel second-order characterizations of important robust stability properties of perturbed Karush-Kuhn-Tucker systems for a broadclass of constrained optimization problems…

Optimization and Control · Mathematics 2020-04-15 Ashkan Mohammadi , Boris Mordukhovich , Ebrahim Sarabi

We consider solutions to degenerate anisotropic elliptic equations in order to study their regularity. In particular we establish second-order estimates and enclose regularity results for the stress field. All our results are new even in…

Analysis of PDEs · Mathematics 2025-03-26 Daniel Baratta , Luigi Muglia , Domenico Vuono

We tackle the problem of building adaptive estimation procedures for ill-posed inverse problems. For general regularization methods depending on tuning parameters, we construct a penalized method that selects the optimal smoothing sequence…

Statistics Theory · Mathematics 2008-07-31 Jean-Michel Loubes , Carenne Ludeña

This paper investigates constrained nonsmooth multiobjective fractional programming problem (NMFP) in real Banach spaces. It derives a quotient calculus rule for computing the first- and second-order Clarke derivatives of fractional…

Optimization and Control · Mathematics 2024-03-18 Jiawei Chen , Luyu Liu , Yibing Lv , Debdas Ghosh , Jen-Chih Yao

We consider nonlinear optimization problems with cardinality constraints. Based on a continuous reformulation we introduce second order necessary and sufficient optimality conditions. Under such a second order condition, we can guarantee…

Optimization and Control · Mathematics 2017-09-06 Max Bucher , Alexandra Schwartz

In this paper, we present new convex relaxations for nonconvex quadratically constrained quadratic programming (QCQP) problems. While recent research has focused on strengthening convex relaxations using reformulation-linearization…

Optimization and Control · Mathematics 2017-09-19 Rujun Jiang , Duan Li

A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…

Dynamical Systems · Mathematics 2019-09-06 Matthew Willis , Kyle T. Alfriend , Simone D'Amico

The resummed expression for the quark form factor illustrates the fact that dimensional continuation provides a regularization not only for ultraviolet and infrared singularities of fixed order QCD amplitudes, but also for the Landau pole…

High Energy Physics - Phenomenology · Physics 2009-10-31 Lorenzo Magnea

We address second-order optimality conditions for optimal control problems involving sparsity functionals which induce spatio-temporal sparsity patterns. We employ the notion of (weak) second subderivatives. With this approach, we are able…

Optimization and Control · Mathematics 2024-12-25 Nicolas Borchard , Gerd Wachsmuth

The goal of this paper is to settle the study of non-commutative optimal transport problems with convex regularization, in their static and finite-dimensional formulations. We consider both the balanced and unbalanced problem and show in…

Mathematical Physics · Physics 2025-06-27 Emanuele Caputo , Augusto Gerolin , Nataliia Monina , Lorenzo Portinale

We classify the complete metrics of nonnegative sectional curvature on M^2xR^2, where M^2 is any compact 2-manifold.

Differential Geometry · Mathematics 2007-05-23 Detlef Gromoll , Kristopher Tapp

A formula for the irregularity of abelian coverings of the projective plane is established and some applications are presented.

Algebraic Geometry · Mathematics 2009-06-01 Daniel Naie

We extend the class of SQP methods for equality constrained optimization to the setting of differentiable manifolds. The use of retractions and stratifications allows us to pull back the involved mappings to linear spaces. We study local…

Optimization and Control · Mathematics 2020-05-15 Anton Schiela , Julian Ortiz

The paper is mainly devoted to systematic developments and applications of geometric aspects of second-order variational analysis that are revolved around the concept of parabolic regularity of sets. This concept has been known in…

Optimization and Control · Mathematics 2020-06-17 Ashkan Mohammadi , Boris S. Mordukhovich , M. Ebrahim Sarabi