In this paper, we focus on the nonconvex-strongly-convex bilevel optimization problem (BLO). In this BLO, the objective function of the upper-level problem is nonconvex and possibly nonsmooth, and …
We study a general convex optimization problem, which covers various classic problems in different areas and particularly includes many optimal transport related problems arising in recent years. T…
The doubly nonnegative (DNN) cone, being the set of all positive semidefinite matrices whose elements are nonnegative, is a popular approximation of the computationally intractable completely posit…
In this paper, we propose a novel adaptive sieving (AS) technique and an enhanced AS (EAS) technique, which are solver independent and can accelerate optimization algorithms for solving large-scale…
In this paper, we consider a class of sparse group ℓ0 regularized optimization problems. First, we give a continuous relaxation model of the considered problem and define a class of stationary po…
This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is to utilize a new parameterizatio…
In this paper, we adopt the augmented Lagrangian method (ALM) to solve convex quadratic second-order cone programming problems (SOCPs). Fruitful results on the efficiency of the ALM have been estab…
We first propose a semi-proximal augmented Lagrangian-based decomposition method to directly solve the primal form of a convex composite quadratic conic-programming problem with a primal block-angu…
Powerful interior-point methods (IPM) based commercial solvers, such as Gurobi and Mosek, have been hugely successful in solving large-scale linear programming (LP) problems. The high efficiency of…
Undirected graphical models have been especially popular for learning the conditional independence structure among a large number of variables where the observations are drawn independently and ide…