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Upcoming Colloquium

On the squared-variable approach for nonlinear (semidefinite) programming
Dr. Lijun Ding, UC San Diego

February 9, 2026
12:30pm-1:30pm via Zoom

Meeting ID: 865 0194 1650

Abstract

Consider min f(x) s.t. x>=0, where the objective function f: R→ R is smooth, and the variable is required to be nonnegative. A naive "squared variable" technique reformulates the problem to min_v f(v^2). Note that the new problem is now unconstrained, and many algorithms, e.g., gradient descent, can be applied. In this talk, we discuss the disadvantages of this approach, which have been known for decades, and demonstrate the surprising advantages: the equivalence for the two problems in terms of (i) local minimizers and (ii) points satisfying the so-called second-order optimality conditions, which are keys for designing optimization algorithms. We further discuss extensions of the approach and equivalence to the vector case (where the vector variable is required to have all entries nonnegative) and the matrix case (where the matrix variable is required to be a positive semidefinite).

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Lijun Ding is an assistant professor at the University of California San Diego. Before that, he was an assistant professor at Texas A&M. He completed his postdoctoral work at the Institute for Foundations of Data Science (IFDS) at the University of Wisconsin and the University of Washington, under the supervision of Stephen J. Wright, Dmitry Drusvyatskiy, and Maryam Fazel. Before joining IFDS, he obtained his Ph.D. in Operations Research from Cornell University, where Yudong Chen and Madeleine Udell advised him. He graduated with an M.S. in Statistics from the University of Chicago, under the advisement of Lek-Heng Lim. He received a B.S. in Mathematics and Economics from the Hong Kong University of Science and Technology.