5 Result(s)
within
Hongbo **ong
Mathematics
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Article
On the Linear Convergence to Weak/Standard d-Stationary Points of DCA-Based Algorithms for Structured Nonsmooth DC Programming
We consider a class of structured nonsmooth difference-of-convex minimization. We allow nonsmoothness in both the convex and concave components in the objective function, with a finite max structure in the con...
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Article
Structural properties of affine sparsity constraints
We introduce a new constraint system for sparse variable selection in statistical learning. Such a system arises when there are logical conditions on the sparsity of certain unknown model parameters that need ...
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Chapter and Conference Paper
Semidefinite Approaches for MIQCP: Convex Relaxations and Practical Methods
We survey several recent advances on applying semidefinite programming (SDP) techniques to globally solve mixed-integer quadratically constrained programs (MIQCPs), or to construct convex relaxations with bett...
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Article
Separating doubly nonnegative and completely positive matrices
The cone of Completely Positive (CP) matrices can be used to exactly formulate a variety of NP-Hard optimization problems. A tractable relaxation for CP matrices is provided by the cone of Doubly Nonnegative (...
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Article
Separation and relaxation for cones of quadratic forms
Let \({P \subseteq \mathfrak{R}_{n}}\) be a pointed, polyhedral cone. In this paper, we study the cone \({\mathcal{C} = {\rm cone}\{xx^T : x \in P\}}\) ...
