基于DNA遗传算法的随机整数规划期望值模型求解

为了求解随机整数规划问题,提出了随机整数规划期望值模型的概念,分析了利用DNA遗传算法求解此类问题的优点,并设计了求解算法,最后通过报童问题,验证了算法的可行性和有效性.     

A novel approach to Bilevel nonlinear programming

Recently developed methods of monotonic optimization have been applied successfully for studying a wide class of nonconvex optimization problems, that includes, among others, generalized polynomial programming, generalized multiplicative and fractional programming, discrete programming, optimization over the efficient set, complementarity problems. In the present paper the monotonic approach is extended to the General Bilevel Programming GBP Problem. It is shown that (GBP) can be transformed into a monotonic optimization problem which can then be solved by “polyblock” approximation or, more efficiently, by a branch-reduce-and-bound method using monotonicity cuts. The method is particularly suitable for Bilevel Convex Programming and Bilevel Linear Programming.      

Algorithms for network piecewise-linear programs: A comparative study

Piecewise-Linear Programming (PLP) is an important area of Mathematical Programming and concerns the minimisation of a convex separable piecewise-linear objective function, subject to linear constraints. In this paper a subarea of PLP called Network Piecewise-Linear Programming (NPLP) is explored. The paper presents four specialised algorithms for NPLP: (Strongly Feasible) Primal Simplex, Dual Method, Out-of-Kilter and (Strongly Polynomial) Cost-Scaling and their relative efficiency is studied. A statistically designed experiment is used to perform a computational comparison of the algorithms. The response variable observed in the experiment is the CPU time to solve randomly generated network piecewise-linear problems classified according to problem class (Transportation, Transshipment and Circulation), problem size, extent of capacitation, and number of breakpoints per arc. Results and conclusions on performance of the algorithms are reported.     

Existence of efficient and properly efficient solutions to problems of constrained vector optimization

Mathematical Programming - The paper is devoted to the existence of global optimal solutions for a general class of nonsmooth problems of constrained vector optimization without boundedness...     

Quadratic geometric programming with application to machining economics

Geometric Programming is extended to include convex quadratic functions. Generalized Geometric Programming is applied to this class of programs to obtain a convex dual program. Machining economics problems fall into this class. Such problems are studied by applying this duality to a nested set of three problems. One problem is zero degree of difficulty and the solution is obtained by solving a simple system of equations. The inclusion of a constraint restricting the force on the tool to be less than or equal to the breaking force provides a more realistic solution. This model is solved as a program with one degree of difficulty. Finally the behavior of the machining cost per part is studied parametrically as a function of axial depth. This research was supported by the Air Force Office of Scientific Research Grant AFOSR-83-0234     

An optimal randomized incremental gradient method

Mathematical Programming - In this paper, we consider a class of finite-sum convex optimization problems whose objective function is given by the average of $$m\, ({\ge }1)$$ smooth components...     

Note on a sufficient condition for a local minimum of a class of nonconvex quadratic programs

A counterexample is given to show that a previously proposed sufficient condition for a local minimum of a class of nonconvex quadratic programs is not correct. This class of problems arises in combinatorial optimization. The problem with the original proof is pointed out. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.     

Strong valid inequalities for a class of concave submodular minimization problems under cardinality constraints

Mathematical Programming - We study the polyhedral convex hull structure of a mixed-integer set which arises in a class of cardinality-constrained concave submodular minimization problems. This...     

Communication-efficient algorithms for decentralized and stochastic optimization

Mathematical Programming - We present a new class of decentralized first-order methods for nonsmooth and stochastic optimization problems defined over multiagent networks. Considering that...     

On univariate function identification problems

Mathematical Programming - Applications in the areas of data fitting, forecasting, and estimation naturally lead to a rich class of constrained infinite-dimensional optimization problems over...     

Fuzzy costs in quadratic programming problems

Although quadratic programming problems are a special class of nonlinear programming, they can also be seen as general linear programming problems. These quadratic problems are of the utmost importance in an increasing variety of practical fields. As, in addition, ambiguity and vagueness are natural and ever-present in real-life situations requiring operative solutions, it makes perfect sense to address them using fuzzy concepts formulated as quadratic programming problems with uncertainty, i.e., as Fuzzy Quadratic Programming problems. This work proposes two novel fuzzy-sets-based methods to solve a particular class of Fuzzy Quadratic Programming problems which have vagueness coefficients in the objective function. Moreover, two other linear approaches are extended to solve the quadratic case. Finally, it is shown that the solutions reached from the extended approaches may be obtained from two proposed parametric multiobjective approaches.     

Ideal formulations for constrained convex optimization problems with indicator variables

Mathematical Programming - Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and...     

Complexity analysis of interior point algorithms for non-Lipschitz and nonconvex minimization

Mathematical Programming - We propose a first order interior point algorithm for a class of non-Lipschitz and nonconvex minimization problems with box constraints, which arise from applications in...     

Second-order variational analysis in second-order cone programming

Mathematical Programming - The paper conducts a second-order variational analysis for an important class of nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream...     

A hybrid stochastic optimization framework for composite nonconvex optimization

Mathematical Programming - We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea...     

Fully polynomial time $$(\Sigma ,\Pi )$$ -approximation schemes for continuous nonlinear newsvendor and continuous stochastic dynamic programs

Mathematical Programming - We study the nonlinear newsvendor problem concerning goods of a non-discrete nature, and a class of stochastic dynamic programs with several application areas such as...     

A reformulation-linearization technique for optimization over simplices

Mathematical Programming - We study non-convex optimization problems over simplices. We show that for a large class of objective functions, the convex approximation obtained from the...     

A Note on Reducing the Number of Variables in Integer Programming Problems

A necessary and sufficient condition for identification of dominatedcolumns, which correspond to one type of redundant integer variables,in the matrix of a general Integer Programming problem, isderived. The given condition extends our recent work on eliminatingdominated integer variables in Knapsack problems, and revises arecently published procedure for reducing the number of variables ingeneral Integer Programming problems given in the literature. Areport on computational experiments for one class of large scaleKnapsack problems, illustrating the function of this approach, isincluded.     

Folded concave penalized sparse linear regression: sparsity,statistical performance,and algorithmic theory for local solutions

Mathematical Programming - This paper concerns the folded concave penalized sparse linear regression (FCPSLR), a class of popular sparse recovery methods. Although FCPSLR yields desirable recovery...     

An improved algorithm for the $$L_2$$ – $$L_p$$ minimization problem

Mathematical Programming - In this paper we consider a class of non-Lipschitz and non-convex minimization problems which generalize the $$L_2$$ – $$L_p$$ minimization problem. We propose an...