On Generalizations of the Frank-Wolfe Theorem to Convex and Quasi-Convex Programmes

In this paper we are concerned with the problem of boundedness and the existence of optimal solutions to the constrained optimization problem. We present necessary and sufficient conditions for boundedness of either a faithfully convex or a quasi-convex polynomial function over the feasible set defined by a system of faithfully convex inequality constraints and/or quasi-convex polynomial inequalities, where the faithfully convex functions satisfy some mild assumption. The conditions are provided in the form of an algorithm, terminating after a finite number of iterations, the implementation of which requires the identification of implicit equality constraints in a homogeneous linear system. We prove that the optimal solution set of the considered problem is nonempty, this way extending the attainability result well known as the so-called Frank-Wolfe theorem. Finally we show that our extension of the Frank-Wolfe theorem immediately implies continuity of the solution set defined by the considered system of (quasi)convex inequalities.     

Minimal representation of quadratically constrained convex feasible regions

In this paper we are concerned with characterizing minimal representations of feasible regions defined by both linear and convex quadratic constraints. We say that representation is minimal if every other representation has either more quadratic constraints, or has the same number of quadratic constraints and at least as many linear constraints. We will prove that a representation is minimal if and only if it contains no redundant constraints, no pseudo-quadratic constraints and no implicit equality constraints. We define a pseudo-quadratic constraint as a quadratic constraint that can be replaced by a finite number of linear constraints. In order to prove the minimal representation theorem, we also prove that if the surfaces of two quadratic constraints match on a ball, then they match everywhere.In this paper we also provide algorithms that can be used to detect implicit equalities and pseudoquadratic constraints. The redundant constraints can be identified using the hypersphere directions (HD) method.Corresponding author.     

Feasible partition problem in reverse convex and convex mixed-integer programming

In this paper we consider the consistent partition problem in reverse convex and convex mixed-integer programming. In particular we will show that for the considered classes of convex functions, both integer and relaxed systems can be partitioned into two disjoint subsystems, each of which is consistent and defines an unbounded region. The polynomial time algorithm to generate the partition will be proposed and the algorithm for a maximal partition will also be provided.     

Exceptional Families and Existence Results for Nonlinear Complementarity Problem

In this paper we establish several sufficient conditions for the existence of a solution to the linear and some classes of nonlinear complementarity problems. These conditions involve a notion of the ``exceptional family of elements' introduced by Smith [19] and Isac, Bulavski and Kalashnikov [4], where the authors have shown that the nonexistence of the ``exceptional family of elements' implies solvability of the complementarity problem. In particular, we establish several sufficient conditions for the nonexistence as well as for the existence of the exceptional family of elements.     

苯二酚异构体的电动毛细管色谱-玻碳微电极柱上安培检测分析方法研究

在玻碳纤维微电极上研究了电解液中β－环糊精（ＣＤ）的浓度对邻、间、对苯二酚的循环伏安特性的影响,从实验结果和分子结构水平方面考察了β－ＣＤ与邻、间、对苯二酚的包结作用。研究结果表明,β－ＣＤ与邻、间、对苯二酚的包结作用强弱顺序为间苯二酚、邻苯二酚、对苯二酚。讨论了电泳缓冲液中ΝΗ４Ｃｌ,ＳＤＳ,β－ＣＤ的浓度及ｐＨ值对邻、间、对苯二酚迁移时间的影响。建立了苯二酚异构体胶束电动毛细管色谱－玻碳微电极柱上安培检测分析方法,方法的回收率在９８％～１０３％之间。     

SOI高温器件及其在汽车电子等领域中的应用

石油钻井,航空航天,汽车等工业领域急需在高温下工作的器件和电路。ＳＯＩ技术在高温器件和电路方面有着广泛的应用前景。文章简要介绍了ＳＯＩ技术应用于制造高温器件和电路方面的进展情况。     

On boundedness of (quasi-)convex integer optimization problems

In this paper we are concerned with the problem of boundedness and the existence of optimal solutions to the constrained integer optimization problem. We present necessary and sufficient conditions for boundedness of either a faithfully convex or quasi-convex polynomial function over the feasible set contained in , and defined by a system of faithfully convex inequality constraints and/or quasi-convex polynomial inequalities. The conditions for boundedness are provided in the form of an implementable algorithm, terminating after a finite number of iterations, showing that for the considered class of functions, the integer programming problem with nonempty feasible region is unbounded if and only if the associated continuous optimization problem is unbounded. We also prove that for a broad class of objective functions (which in particular includes polynomials with integer coefficients), an optimal solution set of the constrained integer problem is nonempty over any subset of .