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Journal of scientific computing, ISSN 1573-7691, 2017, Volume 75, Issue 1, pp. 182 - 197
Journal Article
IEEE transactions on signal processing, ISSN 1941-0476, 2019, Volume 67, Issue 23, pp. 5983 - 5997
We introduce the primal-dual quasi-Newton (PD-QN) method as an approximated second order method for solving decentralized optimization problems... 
quasi-Newton methods | consensus optimization | Multi-agent network | Linear programming | Minimization | primal-dual method | Indexes | Newton method | Optimization | Standards | Convergence | ALGORITHM | ENGINEERING, ELECTRICAL & ELECTRONIC | ADMM
Journal Article
IEEE transactions on automatic control, ISSN 1558-2523, 2019, Volume 64, Issue 7, pp. 2861 - 2868
Journal Article
Computer methods in applied mechanics and engineering, ISSN 0045-7825, 2015, Volume 290, Issue C, pp. 466 - 495
.... The main purpose is the development of a robust and efficient numerical scheme. To enforce crack irreversibility as a constraint, we use a primal-dual active set strategy, which can be identified as a semi-smooth Newton method... 
Phase-field | Fracture mechanics | Primal-dual active set | Predictor- corrector mesh adaptivity | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | CRACK-PROPAGATION | FINITE-ELEMENT APPROXIMATION | BRITTLE-FRACTURE | MODEL | FORMULATION | Predictor-corrector mesh adaptivity | Analysis | Methods | Differential equations | Finite element method | Elastic media | Predictor-corrector methods | Nonlinear dynamics | Mathematical models | Iterative methods | Crack propagation
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2017, Volume 312, pp. 216 - 230
In this paper, we consider a feasible primal–dual interior point method for linear semidefinite programming problem (SDP) based on Alizadeh–Haeberly–Overton (AHO) direction (Monteiro, 1997... 
Primal–dual interior point methods | Central trajectory methods | Linear semidefinite programming | MATHEMATICS, APPLIED | Primal-dual interior point methods | NEWTON-TYPE METHOD | CONVERGENCE | ALGORITHMS | COMPLEMENTARITY | DIRECTIONS | FAMILY | Methods | Algorithms | Numerical analysis | Mathematical analysis | Feasibility | Mathematical models | Displacement | Optimization | Convergence | Mathematical programming | Mathematics | Optimization and Control
Journal Article
Journal Article
Mathematical Programming, ISSN 0025-5610, 01/2011, Volume 126, Issue 1, pp. 1 - 29
... (smooth and/or nonsmooth) minimization reformulations for it. We then discuss first-order methods suitable for solving these reformulations, namely, Nesterov's optimal method... 
Primal-dual first-order methods | Prox-method | Semidefinite programming | Smooth optimal method | Cone programming | Linear programming | Nonsmooth method | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Approximation | Computation | Mathematical analysis | Programming | Minimization | Optimization | Mathematical programming
Journal Article
Journal of computational and applied mathematics, ISSN 0377-0427, 2020, Volume 371, p. 112629
A new numerical method is devised and analyzed for a type of ill-posed elliptic Cauchy problems by using the primal... 
Polygonal or polyhedral meshes | Weak Galerkin | Finite element methods | Weak gradient | Elliptic Cauchy problem | Primal–dual | MATHEMATICS, APPLIED | NONCOERCIVE | Primal-dual
Journal Article
Information and Computation, ISSN 0890-5401, 08/2018, Volume 261, pp. 219 - 239
We develop a dynamic version of the primal-dual method for optimization problems, and apply it to obtain the following results. (1... 
Data structures | Dynamic algorithms | Primal-dual method | MATHEMATICS, APPLIED | VERTEX COVER | COMPUTER SCIENCE, THEORY & METHODS
Journal Article