Thermodynamic performance vs. dynamic stability in an enzymatic reaction model

Previous studies on thermal engine models and energy-converting biological systems have shown that some of the parameters affecting their thermodynamic performance also affect their dynamic stability. In some cases, such parameters represent a tradeoff between these two generic properties. In the present work we carry out a similar analysis on a simple model for an enzymatic reaction. Despite its simplicity, this model captures the essential characteristics of numerous biochemical reactions where an endothermic reaction is made possible by coupling it (via an enzyme) with an exothermic reaction. Our results indicate that the global reaction chemical potential gap () affects both the thermodynamic properties and stability of the steady state. Larger values imply a higher power output and a higher efficiency, but also a less strongly stable steady state.     

Boundary optimal control of the Westervelt and the Kuznetsov equations

This paper is concerned with optimal Neumann boundary control for the Westervelt and the Kuznetsov equations, which are equations of nonlinear acoustics. Specifically, functionals of tracking type with applications in noninvasive ultrasonic medical treatments are considered. Existence of optimal controls is established and first order necessary optimality conditions are derived. Stability of the minimizer with respect to perturbations in the data as well as convergence of the controls when the regularization parameter tends to zero is shown.     

New Second-Order Directional Derivative and Optimality Conditions in Scalar and Vector Optimization

We present a new second-order directional derivative and study its properties. Using this derivative and the parabolic second-order derivative, we establish second-order necessary and sufficient optimality conditions for a general scalar optimization problem by means of the asymptotic and parabolic second-order tangent sets to the feasible set. For the sufficient conditions, the initial space must be finite dimensional. Then, these conditions are applied to a general vector optimization problem obtaining second-order optimality conditions that generalize the differentiable case. For this aim, we introduce a scalarization, and the relationships between the different types of solutions to the vector optimization problem and the scalarized problem are studied. This research was partially supported by the Ministerio de Educación y Ciencia (Spain), under projects MTM2006-02629 and Ingenio Mathematica (i-MATH) CSD2006-00032 (Consolider-Ingenio 2010), and by the Consejería de Educación de la Junta de Castilla y León (Spain), Project VA027B06. The authors are grateful to the anonymous referees for valuable comments and suggestions.     

An optimal Gauss–Markov approximation for a process with stochastic drift and applications

We consider a linear stochastic differential equation with stochastic drift. We study the problem of approximating the solution of such equation through an Ornstein–Uhlenbeck type process, by using direct methods of calculus of variations. We show that general power cost functionals satisfy the conditions for existence and uniqueness of the approximation. We provide some examples of general interest and we give bounds on the goodness of the corresponding approximations. Finally, we focus on a model of a neuron embedded in a simple network and we study the approximation of its activity, by exploiting the aforementioned results.     

Generalized convexity and efficiency for non-regular multiobjective programming problems with inequality-type constraints

For multiobjective problems with inequality-type constraints the necessary conditions for efficient solutions are presented. These conditions are applied when the constraints do not necessarily satisfy any regularity assumptions, and they are based on the concept of 2-regularity introduced by Izmailov. In general, the necessary optimality conditions are not sufficient and the efficient solution set is not the same as the Karush-Kuhn-Tucker points set. So it is necessary to introduce generalized convexity notions. In the multiobjective non-regular case we give the notion of 2-KKT-pseudoinvex-II problems. This new concept of generalized convexity is both necessary and sufficient to guarantee the characterization of all efficient solutions based on the optimality conditions.     

G-pre-invex functions in mathematical programming

In the present paper, we introduce the concept of G-pre-invex functions with respect to η defined on an invex set with respect to η. These function unify the concepts of nondifferentiable convexity, pre-invexity and r-pre-invexity. Furthermore, relationships of G-pre-invex functions to various introduced earlier pre-invexity concepts are also discussed. Some (geometric) properties of this class of functions are also derived. Finally, optimality results are established for optimization problems under appropriate G-pre-invexity conditions.     

On optimality conditions in nondifferentiable programming

This paper is devoted to necessary optimality conditions in a mathematical programming problem without differentiability or convexity assumptions on the data. The main tool of this study is the concept of generalized gradient of a locally Lipschitz function (and more generally of a lower semi-continuous function). In the first part, we consider local extremization problems in the unconstrained case for objective functions taking values in (–, +]. In the second part, the constrained case is considered by the way of the cone of adherent displacements. In the presence of inequality constraints, we derive in the third part optimality conditions in the Kuhn—Tucker form under a constraint qualification.     

超有效元意义下集值优化的最优性条件

该文在Hausdorff局部凸拓扑向量空间考虑约束集值优化问题(SOP)在超有效意义下的Fritz John条件和Kuhn-Tucker条件.首先借助集值映射的下半可微的概念给出这种空间中集值映射导数的定义, 据此讨论了超有效元的Fritz John最优性条件.最后, 给出约束集值优化问题(SOP)取得超有效元的充分条件.     

Dual Bounds and Optimality Cuts for All-Quadratic Programs with Convex Constraints

A central problem of branch-and-bound methods for global optimization is that often a lower bound do not match with the optimal value of the corresponding subproblem even if the diameter of the partition set shrinks to zero. This can lead to a large number of subdivisions preventing the method from terminating in reasonable time. For the all-quadratic optimization problem with convex constraints we present optimality cuts which cut off a given local minimizer from the feasible set. We propose a branch-and-bound algorithm using optimality cuts which is finite if all global minimizers fulfill a certain second order optimality condition. The optimality cuts are based on the formulation of a dual problem where additional redundant constraints are added. This technique is also used for constructing tight lower bounds. Moreover we present for the box-constrained and the standard quadratic programming problem dual bounds which have under certain conditions a zero duality gap.     

Efficient experimental designs when most treatments are unreplicated

In early generation variety trials, large numbers of new breeders’ lines (varieties) may be compared, with each having little seed available. A so-called unreplicated trial has each new variety on just one plot at a site, but includes several replicated control varieties, making up around 10% and 20% of the trial. The aim of the trial is to choose some (usually around one third) good performing new varieties to go on for further testing, rather than precise estimation of their mean yields.Now that spatial analyses of data from field experiments are becoming more common, there is interest in an efficient layout of an experiment given a proposed spatial analysis and an efficiency criterion. Common optimal design criteria values depend on the usual C-matrix, which is very large, and hence it is time consuming to calculate its inverse. Since most varieties are unreplicated, the variety incidence matrix has a simple form, and some matrix manipulations can dramatically reduce the computation needed. However, there are many designs to compare, and numerical optimisation lacks insight into good design features. Some possible design criteria are discussed, and approximations to their values considered. These allow the features of efficient layouts under spatial dependence to be given and compared.