While not convex, this problem can be solved efficiently via singular value decomposition. First, transform the minimization of the Frobenius into a maximization of a matrix-product trace: $$ \max_{R} ...

Spearheaded a comprehensive project on "Optimization Techniques in Convex Functions," delving into root-finding algorithms, Gradient Descent, and Linear Programming. Developed and implemented ...

Magnetic levitation positioning technology has attracted considerable research efforts and dedicated attention due to its extremely attractive features. The technology offers high precision, ...

The method of nonlinear conjugate gradients (NCG) is widely used in practice for unconstrained optimization, but it satisfies weak complexity bounds at best when applied to smooth convex functions. In ...

This chapter helps the students to identify convex functions, convex sets, and convex optimization problems. It presents comparison between a convex and a non‐convex function. The chapter discusses ...

This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses ...

In this paper, we study private optimization problems for non-smooth convex functions on . We show that modifying the exponential mechanism by adding an regularizer to and sampling from recovers both ...