Although robust optimization is a powerful technique in dealing with uncertainty in
optimization, its solutions can be too conservative. More specifically, it can lead to an …

We propose an efficient computational method for linearly constrained quadratic
optimization problems (QOPs) with complementarity constraints based on their Lagrangian …

We propose a conditional gradient framework for a composite convex minimization template
with broad applications. Our approach combines smoothing and homotopy techniques …

Copositivity of tensors plays an important role in vacuum stability of a general scalar
potential, polynomial optimization, tensor complementarity problem and tensor generalized …

We provide a framework for obtaining error bounds for linear conic problems without
assuming constraint qualifications or regularity conditions. The key aspects of our approach …

The completely positive (CP) tensor verification and decomposition are essential in tensor
analysis and computation due to the wide applications in statistics, computer vision …

We present FRA-Poly, a facial reduction algorithm (FRA) for conic linear programs that is
sensitive to the presence of polyhedral faces in the cone. The main goals of FRA and FRA …

In Part I of a series of study on Lagrangian-conic relaxations, we introduce a unified
framework for conic and Lagrangian-conic relaxations of quadratic optimization problems …

This paper considers stochastic convex optimization problems with affine constraints, in
addition to other deterministic convex constraints on the domain of the variables. Usually, to …

Strong (Lagrangian) duality of general conic optimization problems (COPs) has long been
studied and its profound and complicated results appear in different forms in a wide range of …