39 research outputs found
Sufficient conditions for global optimality of bivalent nonconvex quadratic programs with inequality constraints
No full textWe present sufficient conditions for the global optimality of bivalent nonconvex quadratic programs involving quadratic inequality constraints as well as equality constraints. By employing the Lagrangian function, we extend the global subdifferential approach, developed recently in Jeyakumar et al. (J. Glob. Optim., 2007, to appear; Math. Program. Ser. A, 2007, to appear) for studying bivalent quadratic programs without quadratic constraints, and derive global optimality conditions. © 2007 Springer Science+Business Media, LLC.C
Some theoretical aspects of Newton's method for constrained best interpolation
No full textThe paper contains new results as well as surveys on recent developments on the constrained best interpolation problem, and in particular on the convex best interpolation problem. Issues addressed include theoretical reduction of the problem to a system of nonsmooth equations, nonsmooth analysis of those equations and development of Newton's method, convergence analysis and globalization. We frequently use the convex best interpolation to illustrate the seemingly complex theory. Important techniques such as splitting are introduced and interesting links between approaches from approximation and optimization are also established. Open problems related to polyhedral constraints and strips may be tackled by the tools introduced and developed in this paper
CONDITIONS FOR GLOBAL OPTIMALITY OF QUADRATIC MINIMIZATION PROBLEMS WITH LMI CONSTRAINTS
No full textIn this paper we present sufficient conditions for global optimality of non-convex quadratic programs involving linear matrix inequality (LMI) constraints. Our approach makes use of the concept of a quadratic subgradient. We develop optimality conditions for quadratic programs with LMI constraints by using Lagrangian function and by examining conditions which minimizes a quadratic subgradient of the Lagrangian function over simple bounding constraints. As applications, we obtain sufficient optimality condition for quadratic programs with LMI and box constraints by minimizing a quadrtic subgradient over box constraints. We also give optimality conditions for quadratic minimization involving LMI and binary constraints.Quadratic optimization, linear matrix inequalities, box constraints, global optimality, sufficient condition, 41A65, 41A29, 90C30
Conditions for global optimality of quadratic minimization problems with LMI constraints
No full textIn this paper we present sufficient conditions for global optimality of non-convex quadratic programs involving linear matrix inequality (LMI) cnstraints. Our approach makes use of the concept of a quadratic subgradient. We develop optimality conditions for quadratic programs with LMI constraints by using Lagrangian function and by examining conditions which minimizes a quadratic subgradient of the Lagrangian function over simple bounding constraints. As applications, we obtain sufficient optimality condition for quadratic programs with LMI and box constraints by minimizing a quadrtic subgradient over box constraints. We also give optimality conditions for quadratic minimization involving LMI and binary constraints. © World Scientific Publishing Co. & Operational Research Society of Singapore.C
A dual criterion for maximal monotonicity of composition operators
No full textIn this paper we present a dual criterion for the maximal monotonicity of the composition operator T:=A* SA, where S:Y→→ Y is a maximal monotone (set-valued) operator and A: X→ Y is a continuous linear map with the adjoint A*, X and Y are reflexive Banach spaces, and the product notation indicates composition. The dual criterion is expressed in terms of the closure condition involving the epigraph of the conjugate of Fitzpatrick function associated with S, and the operator A. As an easy application, a dual criterion for the maximality of the sum of two maximal monotone operators is also given. © 2006 Springer Science+Business Media B.V.C
Necessary and sufficient conditions for global minimum in multi-extremal global continuous optimization
No full textNecessary and sufficient conditions for global minimum in multi-extremal global continuous optimization. A basic understanding of the mechanisms for finding local "best" (optimal) solutions has been\r\nachieved through optimization techniques. However, solving global optimization problems, where we may have many local optimal solutions which are not the "absolutely best" (global), is vital for many applications in industry & science, and is intrinsically difficult. The lack of verifiable conditions for a global optimum is a serious limitation. This project will develop verifiable such global optimality conditions for many classes of these problems. A new methodology, functional abstract convexity, developed by CIs and has shown promising results, will be extended and applied for solving these problems.$282,474Discovery Project
Mini-implant supported over denture in a patient with down syndrome: a case report
No full textThe presence of macroglossia, a tendency towards poor cooperation and the inability to adapt to compl~te dental prostheses due to motor and mental deficiencies makes the oral rehabilitation of Down Syndrome patients difficult. This article reports on the use of mini implant supported overdenture to rehabilitate a Down Syndrome patient who had difficulty adapting to his new mandibular complete denture. The patient\u27s ability to cooperate during treatment as well as the maintenance of an optimal oral hygiene practice enabled mini-implants to be inserted and maintained 20 months post insertion as evidenced by clinical and radiological findings. To the author\u27s knowledge, this is the first reporting of a successful mini implant supported overdenture in a Down Syndrome patient
