The golden ratio primal-dual algorithm (GRPDA) is a new variant of the classical Arrow--Hurwicz method for solving structured convex optimization problems, in which objective function consists sum two closed proper functions, one involves composition with linear transform. same as and popular (PDA) Chambolle Pock, GRPDA full-splitting sense that it does not rely on any subproblems or system equations iteratively. Compared PDA, an important feature permits larger primal dual stepsizes....

This paper is devoted to two efficient algorithms for solving variational inequality on Hadamard manifolds. The are inspired by Tseng's extragradient methods with new step sizes, established without the knowledge of Lipschitz constant mapping. Under a pseudomonotone assumption underlying vector field, we prove that sequence generated converges solution inequality, whenever it exists.

Higham considered two types of nearest correlation matrix (NCM) problems, namely the W-weighted case and H-weighted case. Since there exists well-defined computable formula for projection onto symmetric positive semidefinite cone under W-weighting, it has been well studied to make several Lagrangian dual-based efficient numerical methods available. But these are not applicable mainly due lack a formula. The remains numerically challenging, especially highly ill-conditioned weight H. In this...

In this paper, we introduce an efficient subgradient extragradient (SE) based method for solving variational inequality problems with monotone operator in Hilbert space. many existing SE methods, two values of are needed over each iteration and the Lipschitz constant or linesearch is required estimating step sizes, which usually not practical expensive. To overcome these drawbacks, present inertial algorithm adaptive estimated by using approximation local without running a linesearch. Each...

In this note, we show a sublinear nonergodic convergence rate for the algorithm developed in Bai et al. [Generalized symmetric ADMM separable convex optimization. Comput Optim Appl. 2018;70:129–170], as well its linear under assumptions that sub-differential of each component objective function is piecewise and all constraint sets are polyhedra. These remaining results established stepsize parameters dual variables belonging to special isosceles triangle region, which aims strengthen our...

In this paper, we present two algorithms for solving equilibrium problems on Hadamard manifolds. The use the extragradient model and golden ratio model, respectively, which are classical models problem in linear space. each iteration, step sizes of only depend value initial parameters information current iteration. Moreover, compared with first algorithm, second algorithm needs to solve one quadratic programming per can greatly reduce computational complexity when structure feasible region...

In this note, we consider three types of problems, H-weighted nearest correlation matrix problem and two important doubly non-negative semidefinite programming, derived from the binary integer quadratic programming maximum cut problem. The dual these problems is a 3-block separable convex optimization with coupling linear equation constraint. It known that, directly extended alternating direction method multipliers (ADMM3d) more efficient than many its variants for solving optimization, but...

In recent years, several convergent variants of the multi-block alternating direction method multipliers (ADMM) have been proposed for solving convex quadratic semidefinite programming via its dual, which is inherently a [Formula: see text]-block separable optimization problem with coupled linear constraints. Among these ADMM-type algorithms, modified ADMM in [Chang, XK, SY Liu and X Li (2016). Modified programming. Neurocomputing, 214, 575–586] bears peculiar feature that augmented...

In this paper, a multi-parameterized proximal point algorithm combining with relaxation step is developed for solving convex minimization problem subject to linear constraints. We show its global convergence and sublinear rate from the prospective of variational inequality. Preliminary numerical experiments on testing sparse signal processing indicate that proposed performs better than some well-established methods.

Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with generic smooth nonbilinear coupling term. Our adaptive strategy works under specific local smoothness conditions, allowing potentially larger stepsizes. For an important class of optimization problems, the proposed reduces to fully proximal gradient without linesearch, thereby representing advancement over golden ratio delineated in...

In order to improve the deficiency generated from uneven distribution of anchors in distributed semidefinite programming (SDP) method, improved method is proposed for solving Euclidean metric localization problems that arise large-scale wireless sensor networks (WSN). By introducing change factorization, nonlinear (NLP) model presented on each subarea, and feasible direction algorithm introduced NLP problems, which can be executed parallel. Numerical results network with more than 10000...

A nonlinear programming (NLP) model with partial orthogonality constraints, relaxed from the polynomial optimization problem, is proposed and analysed for solving sensor network localization. The NLP difficult to solve as constraints are not only non-convex but numerically expensive preserve during iterations. To deal this difficulty, we apply Cayley transform (a Crank–Nicolson-like update scheme) it. Combining gradient descent method, develop a curvilinear search algorithm, analyse its...