Enhancers are short DNA regions bound with activators to increase gene transcription over
long distances. Hence, they play a crucial role in regulating eukaryotic gene expression …

Deep learning algorithms often require solving a highly non-linear and nonconvex
unconstrained optimization problem. Generally, methods for solving the optimization …

Deep learning algorithms often require solving a highly nonlinear and non-convex
unconstrained optimization problem. Methods for solving optimization problems in large …

We present a quasi-Newton method for unconstrained stochastic optimization. Most existing
literature on this topic assumes a setting of stochastic optimization in which a finite sum of …

We present a MATLAB implementation of the symmetric rank-one (SC-SR1) method that
solves trust-region subproblems when a limited-memory symmetric rank-one (L-SR1) matrix …

We propose two limited-memory BFGS (L-BFGS) trust-region methods for large-scale
optimization with linear equality constraints. The methods are intended for problems where …

For optimization problems with linear equality constraints, we prove that the (1, 1) block of
the inverse KKT matrix remains unchanged when projected onto the nullspace of the …

In large-scale optimization, when either forming or storing Hessian matrices are prohibitively
expensive, quasi-Newton methods are often used in lieu of Newton's method because they …

In this work, we consider methods for large-scale and nonconvex unconstrained
optimization. We propose a new trust-region method whose subproblem is defined using a …

We present a modified limited memory BFGS (L-BFGS) method that converges globally and
linearly for nonconvex objective functions. Its distinguishing feature is that it turns into L …