An exact penalty global optimization approach for mixed-integer programming problems

In this work, we propose a global optimization approach for mixed-integer programming problems. To this aim, we preliminarily define an exact penalty algorithm model for globally solving general problems and we show its convergence properties. Then, we describe a particular version of the algorithm that solves mixed-integer problems and we report computational results on some MINLP problems.     

Well-posedness for parametric optimization problems with variational inclusion constraint

In this paper, we study the well-posedness for the parametric optimization problems with variational inclusion problems as constraint (or the perturbed problem of optimization problems with constraint). Furthermore, we consider the relation between the well-posedness for the parametric optimization problems with variational inclusion problems as constraint and the well-posedness in the generalized sense for variational inclusion problems.     

伪单调型向量F-互补问题可行集的最小元问题

本文引入了几类向量F-互补问题并给出了向量F-互补问题与广义向量变分不等式之间的关系.通过定义向量F-互补问题的可行集,研究了伪单调型向量F-互补问题的可行集的最小问题,推广了已有的一些结果.     

A nonasymptotic method for general linear singular perturbation problems

The nonasymptotic method developed in Ref. 1 has been extended for solving general linear singularly perturbed two-point boundary-value problems. Firstly, we discuss problems with a right-hand boundary layer. Secondly, we discuss problems with an interior layer. Finally, we discuss problems with two boundary layers. Numerical experience with the method for some model problems is also reported to confirm the theoretical analysis.     

Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty

In this paper we examine non-convex quadratic optimization problems over a quadratic constraint under unknown but bounded interval perturbation of problem data in the constraint and develop criteria for characterizing robust (i.e. uncertainty-immunized) global solutions of classes of non-convex quadratic problems. Firstly, we derive robust solvability results for quadratic inequality systems under parameter uncertainty. Consequently, we obtain characterizations of robust solutions for uncertain homogeneous quadratic problems, including uncertain concave quadratic minimization problems and weighted least squares. Using homogenization, we also derive characterizations of robust solutions for non-homogeneous quadratic problems.     

Qualitative and quantitative data envelopment analysis with interval data

In this paper, we investigate DEA with interval input-output data. First we show various extensions of efficiency and that 25 of them are essential. Second we formulate the efficiency test problems as mixed integer programming problems. We prove that 14 among 25 problems can be reduced to linear programming problems and that the other 11 efficiencies can be tested by solving a finite sequence of linear programming problems. Third, in order to obtain efficiency scores, we extend SBM model to interval input-output data. Fourth, to moderate a possible positive overassessment by DEA, we introduce the inverted DEA model with interval input-output data. Using efficiency and inefficiency scores, we propose a classification of DMUs. Finally, we apply the proposed approach to Japanese Bank Data and demonstrate its advantages.     

Global optimization in stabilizing controller design

In this paper, we develop a global optimization methodology to solve stabilization problems. We first formulate stabilization problems as bilevel programming problems. By invoking the Hurwitz stability conditions, we reformulate these bilevel programs to equivalent single-level nonconvex optimization programs. The branch-and-reduce global optimization algorithm is finally applied to these problems. Using the proposed methodology, we report improved solutions for two feedback stabilization problems from the literature. In addition, we improve the lower bound of the stabilizability parameter of the Belgian chocolate problem from the previous best known 0.96 to 0.973974.     

The studies of systems of variational inclusions problems and variational disclusions problems with applications

In this paper, we study existence theorems of solutions for systems of variational inclusions problems and systems of variational disclusions problems. From these existence results, we establish existence theorems of solutions for systems of generalized vector quasiequilibrium problems and systems of quasioptimization problems.     

运输问题的退化解及表解中0元的添加

在运输问题表上作业法中,有时会遇到退化解问题,这样在给调运方案时需要在调运表上添加0元,可是0应添在何处?大多数文献中均未具体给出或给出的结论有误,0元的添加不当有时会导致一系列问题出现,本文将讨论这些问题,且给出一个0元添加的确定的答案.     

Convergence Theorem for Variational Inequality in Hilbert Spaces with Applications

In this paper, we study variational inequality over the set of the common fixed points of a countable family of quasi-nonexpansive mappings. To tackle this problem, we propose an algorithm and use it to prove a strong convergence theorem under suitable conditions. As applications, we study variational inequality over the solution set of different nonlinear or linear problems, like minimization problems, split feasibility problems, convexly pseudoinverse problems, convex linear inverse problems, etc.     

Isomorphic scheduling problems

We consider general properties of isomorphic scheduling problems that constitute a new class of pairs of mutually related scheduling problems. Any such a pair is composed of a scheduling problem with fixed job processing times and its time-dependent counterpart with processing times that are proportional-linear functions of the job starting times. In order to introduce the class formally, first we formulate a generic scheduling problem with fixed job processing times and define isomorphic problems by a one-to-one transformation of instances of the generic problem into instances of time-dependent scheduling problems with proportional-linear job processing times. Next, we prove basic properties of isomorphic scheduling problems and show how to convert polynomial algorithms for scheduling problems with fixed job processing times into polynomial algorithms for proportional-linear counterparts of the original problems. Finally, we show how are related approximation algorithms for isomorphic problems. Applying the results, we establish new worst-case results for time-dependent parallel-machine scheduling problems and prove that many single- and dedicated-machine time-dependent scheduling problems with proportional-linear job processing times are polynomially solvable.     

An efficient method for solving nonlocal initial-boundary value problems for linear and nonlinear first-order hyperbolic partial differential equations

In this paper, we present a new approach to solve nonlocal initial-boundary value problems of linear and nonlinear hyperbolic partial differential equations of first-order subject to initial and nonlocal boundary conditions of integral type. We first transform the given nonlocal initial-boundary value problems into local initial-boundary value problems. Then we apply a modified Adomian decomposition method, which permits convenient resolution of these problems. Moreover, we prove this decomposition scheme applied to such nonlocal problems is convergent in a suitable Hilbert space, and then extend our discussion to include systems of first-order linear equations and other related nonlocal initial-boundary value problems.     

Mixed generalized quasi-equilibrium problems

In this paper, we introduce mixed generalized quasi-equilibrium problems and show some sufficient conditions on the existence of their solutions. As special cases, we obtain several results for different mixed quasi-equilibrium problems, mixed quasi-variational inclusions problems and mixed quasi-relation problems etc.     

On System of Generalized Vector Quasi-equilibrium Problems with Set-valued Maps

In this paper, we introduce four new types of the system of generalized vector quasi-equilibrium problems with set-valued maps which include system of vector quasi-equilibrium problems, system of vector equilibrium problems, system of variational inequality problems, and vector equilibrium problems in the literature as special cases. We prove the existence of solutions for such kinds of system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of vector quasi-equilibrium problems and the generalized Debreu type equilibrium problem for vector-valued functions.     

Well-posedness of variational problems with applications to staircase methods

In this Note we extend the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, for inclusion and fixed-point problems. Then we investigate conditions under which we have equivalence for this concept between the different problems. An application to methods coupling iteration and approximation is presented.     

具有混合型边界条件的左定Sturm-Liouville问题特征值的下标计算(英文)

本文研究具有混合型边界条件的左定Sturm-Liouvile问题特征值的下标计算问题.首先给出具有分离型边界条件和混合型边界条件的左定Sturm-Liouville问题的特征值之间的不等式;然后利用这个结果给出一种计算混合型边界条件下左定Sturm-Liouville问题特征值下标的方法.     

Fuzzy linear programming problems as bi-criteria optimization problems

In this paper, we consider fuzzy linear programming (FLP) problems which involve fuzzy numbers only in coefficients of objective function. First, we shall give concepts of optimal solutions to (FLP) problems and investigate their properties. Next, in order to find all optimal solutions, we define three types of bi-criteria optimization problems.     

The Million-Variable “March” for Stochastic Combinatorial Optimization

Combinatorial optimization problems have applications in a variety of sciences and engineering. In the presence of data uncertainty, these problems lead to stochastic combinatorial optimization problems which result in very large scale combinatorial optimization problems. In this paper, we report on the solution of some of the largest stochastic combinatorial optimization problems consisting of over a million binary variables. While the methodology is quite general, the specific application with which we conduct our experiments arises in stochastic server location problems. The main observation is that stochastic combinatorial optimization problems are comprised of loosely coupled subsystems. By taking advantage of the loosely coupled structure, we show that decomposition-coordination methods provide highly effective algorithms, and surpass the scalability of even the most efficiently implemented backtracking search algorithms.     

Existence Theorems of Simultaneous Equilibrium Problems and Generalized Vector Quasi-Saddle Points

In this paper, we establish the existence theorems of simultaneous equilibrium problems. As consequences of our results, we establish the existence theorem of simultaneous mathematical programs and equilibrium problems and the existence theorems of generalized vector quasi-saddle point problems.     

Scalarization and optimality conditions for vector equilibrium problems

In this paper, we investigated vector equilibrium problems and gave the scalarization results for weakly efficient solutions, Henig efficient solutions, and globally efficient solutions to the vector equilibrium problems without the convexity assumption. Using nonsmooth analysis and the scalarization results, we provided the necessary conditions for weakly efficient solutions, Henig efficient solutions, globally efficient solutions, and superefficient solutions to vector equilibrium problems. By the assumption of convexity, we gave sufficient conditions for those solutions. As applications, we gave the necessary and sufficient conditions for corresponding solutions to vector variational inequalities and vector optimization problems.