Isaac Siwale

Partial Relaxation of Equality-constrained Programs

  • Isaac Siwale
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    This paper presents a reformulation that is a natural “by-product” of the ‘variable endogenization’ process for equality-constrained programs. The method results a partial relaxation of the constraints which in turn confers some computational advantages. A fully-annotated example illustrates the technique and presents some comparative numerical results. Citation Siwale, I.: Partial Relaxation of Equality-constrained Programs. Technical … Read more

    Global Optimization via Slack Variables

  • Isaac Siwale
    • Categories Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    This paper presents a method for finding global optima to constrained nonlinear programs via slack variables. The method only applies if all functions involved are of class C1 but without any further qualification on the types of constraints allowed; it proceeds by reformulating the given program into a bi-objective program that is then solved for … Read more

    On Global Optimization

  • Isaac Siwale
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization Tags , , , ,

    This paper presents a relatively “unfettered” method for finding global optima to constrained nonlinear programs. The method reformulates the given program into a bi-objective mixed-integer program that is then solved for the Nash equilibrium. A numerical example (whose solution provides a new benchmark against which other algorithms may be assessed) is included to illustrate the … Read more

    Practical Portfolio Optimization

  • Isaac Siwale
    • Categories Applications - OR and Management Sciences, Finance and Economics

    This paper is on the portfolio optimization problem for which two generic models are presented in the context of a proprietary solver called GENO: the first is a pseudo-dynamic model meant for the single holding-period case; the second is a truly dynamic model that applies to both the single and the multi-period scenario. Both models … Read more

    Solution of Nonlinear Equations via Optimization

  • Isaac Siwale
    • Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Multi-Criteria Optimization Tags , , , , ,

    This paper presents four optimization models for solving nonlinear equation systems. The models accommodate both over-specified and under-specified systems. A variable endogenization technique that improves efficiency is introduced, and a basic comparative study shows one of the methods presented to be very effective. Citation Siwale, I. (2013). Solution of nonlinear equation systems via optimization. Technical … Read more

    Practical Multi-objective Programming

  • Isaac Siwale
    • Categories Applications - OR and Management Sciences Tags , , , , ,

    This paper is on practical solutions to the multi-objective optimization problem; it advocates for single-point solutions either of the Nash equilibrium or the Tchebycheff compromise type, depending on whether one can reasonably ascribe competition or cooperation to the problem at hand. A transform method that greatly simplifies implementation of the compromise solution is presented and … Read more