Extreme point Quadratic Minimization Problem

1993 ◽  
Vol 14 (1) ◽  
pp. 73-81
Author(s):  
Renu Gupta ◽  
M. C. Puri
Keyword(s):  
Extreme Point ◽  
Minimization Problem ◽  
Quadratic Minimization

scholarly journals A NEW APPROACH TO LINEAR SHELL THEORY

2005 ◽  
Vol 15 (08) ◽  
pp. 1181-1202 ◽  
Author(s):  
PHILIPPE G. CIARLET ◽  
LILIANA GRATIE
Keyword(s):  
Vector Field ◽  
Minimization Problem ◽  
Shell Theory ◽  
Displacement Vector ◽  
Constrained Minimization ◽  
New Approach ◽  
Quadratic Minimization ◽  
Displacement Vector Field ◽  
Constrained Minimization Problem ◽  
Linear Shell Theory

We propose a new approach to the existence theory for quadratic minimization problems that arise in linear shell theory. The novelty consists in considering the linearized change of metric and change of curvature tensors as the new unknowns, instead of the displacement vector field as is customary. Such an approach naturally yields a constrained minimization problem, the constraints being ad hoc compatibility relations that these new unknowns must satisfy in order that they indeed correspond to a displacement vector field. Our major objective is thus to specify and justify such compatibility relations in appropriate function spaces. Interestingly, this result provides as a corollary a new proof of Korn's inequality on a surface. While the classical proof of this fundamental inequality essentially relies on a basic lemma of J. L. Lions, the keystone in the proposed approach is instead an appropriate weak version of a classical theorem of Poincaré. The existence of a solution to the above constrained minimization problem is then established, also providing as a simple corollary a new existence proof for the original quadratic minimization problem.

scholarly journals Global Sufficient Optimality Conditions for a Special Cubic Minimization Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaomei Zhang ◽  
Yanjun Wang ◽  
Weimin Ma
Keyword(s):  
Optimality Conditions ◽  
Minimization Problem ◽  
Sufficient Conditions ◽  
Sufficient Optimality Conditions ◽  
Global Optimality ◽  
Global Optimality Conditions ◽  
Box Constraints ◽  
Global Minimizers ◽  
Quadratic Minimization ◽  
Binary Constraints

We present some sufficient global optimality conditions for a special cubic minimization problem with box constraints or binary constraints by extending the global subdifferential approach proposed by V. Jeyakumar et al. (2006). The present conditions generalize the results developed in the work of V. Jeyakumar et al. where a quadratic minimization problem with box constraints or binary constraints was considered. In addition, a special diagonal matrix is constructed, which is used to provide a convenient method for justifying the proposed sufficient conditions. Then, the reformulation of the sufficient conditions follows. It is worth noting that this reformulation is also applicable to the quadratic minimization problem with box or binary constraints considered in the works of V. Jeyakumar et al. (2006) and Y. Wang et al. (2010). Finally some examples demonstrate that our optimality conditions can effectively be used for identifying global minimizers of the certain nonconvex cubic minimization problem.

scholarly journals The golden target: analyzing the tracking performance of leveraged gold ETFs

2015 ◽  
Vol 32 (3) ◽  
pp. 278-297 ◽  
Author(s):  
Tim Leung ◽  
Brian Ward
Keyword(s):  
Minimization Problem ◽  
Design Methodology ◽  
Detailed Comparison ◽  
Tracking Performance ◽  
Exchange Traded Funds ◽  
Tracking Errors ◽  
Content Type ◽  
Leverage Ratio ◽  
Quadratic Minimization ◽  
Gold Futures

Purpose – The purpose of this study is to understand the tracking errors of leveraged exchange-traded funds (LETFs) on gold and demonstrate improved tracking performance by dynamic portfolios of gold futures. Design/methodology/approach – The author formulates and solves a constrained quadratic minimization problem to construct static replicating portfolios of both leveraged and unleveraged benchmarks in gold; a dynamic constant leveraged portfolio using gold futures is used to track the path of the leveraged gold benchmark. Findings – The results suggest that market-traded LETFs do not track a leveraged position in gold effectively over a long horizon, and the dynamic leveraged futures portfolio achieves lower tracking errors over multiple years. Research limitations/implications – The research informs us that investors should consider alternative portfolios with gold futures, rather than holding a leveraged gold exchange-traded funds to achieve a desired leveraged exposure in spot gold. Originality/value – The main contribution of the study is the use of gold futures to dynamically replicate a gold benchmark with any given leverage ratio and the detailed comparison of the tracking performance of LETFs versus optimal static and dynamic futures portfolios.

LAGRANGE MULTIPLIERS IN INTRINSIC ELASTICITY

2011 ◽  
Vol 21 (04) ◽  
pp. 651-666 ◽  
Author(s):  
PHILIPPE G. CIARLET ◽  
PATRICK CIARLET ◽  
OANA IOSIFESCU ◽  
STEFAN SAUTER ◽  
JUN ZOU
Keyword(s):  
Saddle Point ◽  
Minimization Problem ◽  
Tensor Field ◽  
Ad Hoc ◽  
Displacement Vector ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Quadratic Minimization ◽  
Linearized Elasticity ◽  
Potential Applications

In an intrinsic approach to three-dimensional linearized elasticity, the unknown is the linearized strain tensor field (or equivalently the stress tensor field by means of the constitutive equation), instead of the displacement vector field in the classical approach. We consider here the pure traction problem and the pure displacement problem and we show that, in each case, the intrinsic approach leads to a quadratic minimization problem constrained by Donati-like relations (the form of which depends on the type of boundary conditions considered). Using the Babuška-Brezzi inf-sup condition, we then show that, in each case, the minimizer of the constrained minimization problem found in an intrinsic approach is the first argument of the saddle-point of an ad hoc Lagrangian, so that the second argument of this saddle-point is the Lagrange multiplier associated with the corresponding constraints. Such results have potential applications to the numerical analysis and simulation of the intrinsic approach to three-dimensional linearized elasticity.

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