Chee-Khian Sim

An optimizer/operational researcher with numerous years of experience in teaching fundamental mathematics and advanced operational research courses, and academic research experience in modelling, solving optimisation problems, with industrial experience in information technology.

Refining asymptotic complexity bounds for nonconvex optimization methods, including why steepest descent is o(eps^{-2}) rather than O(eps^{-2})

  • Serge Gratton
  • Chee-Khian Sim
  • Philippe L. Toint
    • Categories Nonlinear Optimization Tags ,

    \(\) We revisit the standard “telescoping sum” argument ubiquitous in the final steps of analyzing evaluation complexity of algorithms for smooth nonconvex optimization, and obtain a refined formulation of the resulting bound as a function of the requested accuracy eps. While bounds obtained using the standard argument typically are of the form \(O(\epsilon^{-\alpha})\) for some … Read more

    Superlinear convergence of an interior point algorithm on linear semi-definite feasibility problems

  • Chee-Khian Sim
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , , ,

    In the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual or the NT direction, to solve semi-definite programs (SDPs) is shown by (i) assuming that the given SDP is nondegenerate and making modifications to these algorithms [10], or … Read more

    Solution to a Monotone Inclusion Problem using the Relaxed Peaceman-Rachford Splitting Method: Convergence and its Rates

  • Chee-Khian Sim
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    We consider the convergence behavior using the relaxed Peaceman-Rachford splitting method to solve the monotone inclusion problem $0 \in (A + B)(u)$, where $A, B: \Re^n \rightrightarrows \Re^n$ are maximal $\beta$-strongly monotone operators, $n \geq 1$ and $\beta > 0$. Under a technical assumption, convergence of iterates using the method on the problem is proved … Read more

    A FISTA-type first order algorithm on composite optimization problems that is adaptable to the convex situation

  • Chee-Khian Sim
    • Categories Nonsmooth Optimization

    In this note, we propose a FISTA-type first order algorithm, VAR-FISTA, to solve a composite optimization problem. A distinctive feature of VAR-FISTA is its ability to exploit the convexity of the function in the problem, resulting in an improved iteration complexity when the function is convex compared to when it is nonconvex. The iteration complexity … Read more

    A FISTA-type accelerated gradient algorithm for solving smooth nonconvex composite optimization problems

  • Jiaming Liang
  • Renato D.C. Monteiro
  • Chee-Khian Sim
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    In this paper, we describe and establish iteration-complexity of two accelerated composite gradient (ACG) variants to solve a smooth nonconvex composite optimization problem whose objective function is the sum of a nonconvex differentiable function f with a Lipschitz continuous gradient and a simple nonsmooth closed convex function h. When f is convex, the first ACG … Read more

    Interior Point Method on Semi-definite Linear Complementarity Problems using the Nesterov-Todd (NT) Search Direction: Polynomial Complexity and Local Convergence

  • Chee-Khian Sim
    • Categories Semi-definite Programming

    We consider in this paper an infeasible predictor-corrector primal-dual path following interior point algorithm using the Nesterov-Todd (NT) search direction to solve semi-definite linear complementarity problems. Global convergence and polynomial iteration complexity of the algorithm are established. Two sufficient conditions are also given for superlinear convergence of iterates generated by the algorithm. Preliminary numerical results … Read more

    Policies for Inventory Models with Product Returns Forecast from Past Demands and Past Sales

  • Mabel C. Chou
  • Chee-Khian Sim
  • Xiao-Ming Yuan
    • Categories Dynamic Programming, Supply Chain Management

    Finite horizon periodic review backlog models are considered in this paper for an inventory system that remanufactures two types of cores: buyback cores and normal cores. Returns of used products as buyback cores are modelled to depend on past demands and past sales. We obtain an optimal inventory policy for the model in which returns … Read more

    Complexity of the relaxed Peaceman-Rachford splitting method for the sum of two maximal strongly monotone operators

  • Renato D.C. Monteiro
  • Chee-Khian Sim
    • Categories Convex and Nonsmooth Optimization

    This paper considers the relaxed Peaceman-Rachford (PR) splitting method for fi nding an approximate solution of a monotone inclusion whose underlying operator consists of the sum of two maximal strongly monotone operators. Using general results obtained in the setting of a non-Euclidean hybrid proximal extragradient framework, convergence of the iterates, as well as pointwise and ergodic … Read more

    Infinite horizon optimal policy for an inventory system with two types of products sharing common hardware platforms

  • Mabel C. Chou
  • Chee-Khian Sim
  • Xiao-Ming Yuan
    • Categories Applications - OR and Management Sciences

    We consider a periodic review inventory system and present its optimal policy in the infinite horizon setting. The optimal inventory policy that maximizes the infinite horizon expected discount profit for the model is analytically obtained by relating to the finite horizon setting using results from variational analysis. Results are provided that elucidate the operations of … Read more

    On Finding a Generalized Lowest Rank Solution to a Linear Semi-definite Feasibility Problem

  • Chee-Khian Sim
    • Categories Linear, Cone and Semidefinite Programming

    In this note, we generalize the affine rank minimization problem and the vector cardinality minimization problem and show that the resulting generalized problem can be solved by solving a sequence of continuous concave minimization problems. In the case of the vector cardinality minimization problem, we show that it can be solved by solving the continuous … Read more