Decomposed Structured Subsets for Semidefinite Optimization

Optimization over Structured Subsets of Positive Semidefinite Matrices via Column Generation

We develop algorithms to construct inner approximations of the cone of positive semidefinite matrices via linear programming and second order cone programming. Starting with an initial linear algebraic approximation suggested recently by Ahmadi and Majumdar, we describe an iterative process through which our approximation is improved at every step. This is done using ideas from column generatio...

Supplement: Efficient Decomposed Learning for Structured Prediction

This supplement provides the proof for all the theorems and corollaries in the main paper. We provide the proofs as well as the theorem statements for the ease of understanding while borrowing the notation from the main draft. Proof. Assume that we are given an > 0 for which the condition mentioned in the theorem statement holds true (for the sake of simplicity we assume the same for all w ∈ R ...

Efficient Decomposed Learning for Structured Prediction

Structured prediction is the cornerstone of several machine learning applications. Unfortunately, in structured prediction settings with expressive inter-variable interactions, exact inference-based learning algorithms, e.g. Structural SVM, are often intractable. We present a new way, Decomposed Learning (DecL), which performs efficient learning by restricting the inference step to a limited pa...

Semidefinite Optimization

Semidefinite Optimization ∗

Optimization problems in which the variable is not a vector but a symmetric matrix which is required to be positive semidefinite have been intensely studied in the last ten years. Part of the reason for the interest stems from the applicability of such problems to such diverse areas as designing the strongest column, checking the stability of a differential inclusion, and obtaining tight bounds...