Research

Dr. Sun has a wide range of interests in both theory and applications of deterministic optimization and optimization under uncertainty.

• On deterministic optimization, Dr. Sun's recent research has focused on
  • Convex relaxations for nonconvex optimization problems over a network:
    • We develop a new matrix minor based reformulation of rank constraints.
    • The matrix minor constraints correspond to two-cycles (an edge), three-cycles, and four-cycles in the network, so network sparsity is naturally explored.
    • Second-order conic programming and linear programming based relaxations are developed for minor constraints.
    • Resulting convex relaxations can be both significantly faster and stronger than SDP relaxations.
  • Distributed algorithms for constrained nonconvex optimization with global convergence guarantees:
    • We demonstrate why ADMM-type algorithms cannot guarantee convergence for solving nonconvex optimization with complicated nonconvex nonsmooth constraints regardless how the centralized problem is reformulated,
    • We propose a new two-level distributed algorithm for solving nonconvex optimization with complicated nonconvex nonsmooth constraints.
    • Applications are broad: nonconvex network flows, nonconvex consensus optimization, general nonsmooth nonconvex constrained programs, etc.
  • Certification of existence and uniqueness of solutions of nonlinear equations via complex fixed point theory:
    • We develop a general method for proving existence and uniqueness of complex fixed point of a holomorphic function in several complex variables. Region of attraction and linear convergence rate of the fixed point iterations are also characterized.
    • The general theory is applied to provide existence and uniqueness conditions for power flow equations. The resulting condition is in the form: If the load real and reactive power satisfies a certain condition, then there exists a unique voltage solution in a prescribed polydisc and no voltage solution exists outside the polydisc in a larger region (could be a polydisc, a half-space, or the outside of a polydisc).
    • Our result is provably tighter and empirically much stronger than other existing conditions, and completely characterizes the loadability region of the fundamental 2-bus system for the first time.
  • Mixed integer nonlinear programming, strong cuts, and spatial dynamical programming:
    • Motivated by the natural gas transient problem, a notoriously difficult problem, we develop a general algorithmic framework for obtaining upper and lower bounds for a MINLP with complicated nonlinear nonconvex constraints.
    • The key new techniques include:
      • A spatial DP decomposition framework;
      • Augmented Lagrangian relaxations with nonconvex cuts;
      • Convergence rate analysis -- the developed framework encompasses any tree-based forward-backward methods such as SDDP or SDDiP.
• On the uncertainty side, Dr. Sun has developed the first efficient algorithm for solving two-stage robust optimization problems that is much faster than Benders decomposition, cutting plane methods for multistage robust linear optimization much scalable than duality approach, models for decision-dependent uncertainty, and recently a fast exact algorithm (SDDiP) for multistage stochastic integer programming. His team is working toward developing efficient algorithms for multistage robust and stochastic programs with integer decisions.
• On the application side, Dr. Sun has extensively worked on core optimization problems for electric power system operations and planning, and collaborated with major utility companies and system operators in the US. Dr. Sun's work on robust optimization for the Unit Commitment problem and strong convexification for optimal power flow problems have attracted substantial interests and follow-up research both in industry and academia.