Multicriterion decision making in river basin planning and development

Five Multicriterion Decision Making (MCDM) methods, namely, ELECTRE-2, PROMETHEE-2, Analytic Hierarchy Process (AHP), Compromise Programming (CP) and EXPROM-2 are employed to select the best reservoir configuration for the case study of Chaliyar river basin, Kerala, India. Spearman rank correlation coefficient is used to assess the correlation between the ranks obtained by the above MCDM methods. Although, these methods follow different approaches, the analysis has shown that the same preference strategy is reached by all the methods. Comparative evaluation of MCDM methods revealed that Compromise Programming is best suited for the present case study.     

A comparison of genetic and conventional methods for the solution of integer goal programmes

This paper discusses two different approaches to the solution of difficult Goal Programming (GP) models. An integer Goal Programming (IGP) solver and some genetically driven multi-objective methods are developed. Specialised GP speed up techniques and analysis tools are employed in the design and development of the solution systems. A selection of linear integer models of small to medium size with an internal structure that makes solution difficult are considered. These problems are solved by both methods in order to assess their computational performance over several criteria and to compare the differences between them. From the results obtained in this research, it is observed that genetic algorithms (GA) have performed in general less efficiently than the Integer Goal Programming system for the sample of problems analysed.     

Using regularization and second order information in outer approximation for convex MINLP

Mathematical Programming - In this paper, we present two new methods for solving convex mixed-integer nonlinear programming problems based on the outer approximation method. The first method is...     

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.      

Integrating the use of linear and dynamic programming methods for dairy cow diet formulation

Despite many refinements that have been made to the basic Linear Programming model used to find economically optimal diets for dairy cows, the sequential nature of the physical and physiological changes that a cow goes through during lactation have not been incorporated into the modelling process satisfactorily. This paper demonstrates how it can be achieved by integrating the use of both Linear and Dynamic Programming methods to optimise the economic performance of a dairy cow over its entire lactation. Linear Programming generates solutions for each potential liveweight change occurring during each of eleven four week periods over the lactation, then the use of DP allows both the selection of the optimal sequence of liveweight changes during the lactation and the specification of rations associated with this optimal path.     

The use of goal programming and data envelopment analysis for estimating efficient marginal costs of outputs

The paper concerns the use of alternative and/or combined methodologies (Data Envelopment Analysis, Regression Analysis, Goal Programming) as a means of ascertaining the efficiency as well as the efficient marginal costs of outputs of homogeneous organizational units. The same body of data is used throughout the analysis and the results derived from the combination of Data Envelopment Analysis and Goal Programming are shown to be more reliable than those obtained by the other methods.     

Integrating SQP and Branch-and-Bound for Mixed Integer Nonlinear Programming

This paper considers the solution of Mixed Integer Nonlinear Programming (MINLP) problems. Classical methods for the solution of MINLP problems decompose the problem by separating the nonlinear part from the integer part. This approach is largely due to the existence of packaged software for solving Nonlinear Programming (NLP) and Mixed Integer Linear Programming problems.In contrast, an integrated approach to solving MINLP problems is considered here. This new algorithm is based on branch-and-bound, but does not require the NLP problem at each node to be solved to optimality. Instead, branching is allowed after each iteration of the NLP solver. In this way, the nonlinear part of the MINLP problem is solved whilst searching the tree. The nonlinear solver that is considered in this paper is a Sequential Quadratic Programming solver.A numerical comparison of the new method with nonlinear branch-and-bound is presented and a factor of up to 3 improvement over branch-and-bound is observed.     

Quasi-Monte Carlo methods for two-stage stochastic mixed-integer programs

Mathematical Programming - We consider randomized QMC methods for approximating the expected recourse in two-stage stochastic optimization problems containing mixed-integer decisions in the second...     

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...     

Riemannian Optimization via Frank-Wolfe Methods

Mathematical Programming - We study projection-free methods for constrained Riemannian optimization. In particular, we propose a Riemannian Frank-Wolfe (RFW) method that handles constraints...     

A frequency-domain analysis of inexact gradient methods

Mathematical Programming - We study robustness properties of some iterative gradient-based methods for strongly convex functions, as well as for the larger class of functions with sector-bounded...     

From differential equation solvers to accelerated first-order methods for convex optimization

Mathematical Programming - Convergence analysis of accelerated first-order methods for convex optimization problems are developed from the point of view of ordinary differential equation solvers. A...     

Stochastic quasi-gradient methods: variance reduction via Jacobian sketching

Mathematical Programming - We develop a new family of variance reduced stochastic gradient descent methods for minimizing the average of a very large number of smooth functions. Our...     

Newton acceleration on manifolds identified by proximal gradient methods

Mathematical Programming - Proximal methods are known to identify the underlying substructure of nonsmooth optimization problems. Even more, in many interesting situations, the output of a...     

Stopping criteria for,and strong convergence of,stochastic gradient descent on Bottou-Curtis-Nocedal functions

Mathematical Programming - Stopping criteria for Stochastic Gradient Descent (SGD) methods play important roles from enabling adaptive step size schemes to providing rigor for downstream analyses...     

Variance reduction for root-finding problems

Mathematical Programming - Minimizing finite sums of smooth and strongly convex functions is an important task in machine learning. Recent work has developed stochastic gradient methods that...     

Rates of superlinear convergence for classical quasi-Newton methods

Mathematical Programming - We study the local convergence of classical quasi-Newton methods for nonlinear optimization. Although it was well established a long time ago that asymptotically these...     

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...     

Principled analyses and design of first-order methods with inexact proximal operators

Mathematical Programming - Proximal operations are among the most common primitives appearing in both practical and theoretical (or high-level) optimization methods. This basic operation typically...     

An elementary approach to tight worst case complexity analysis of gradient based methods

Mathematical Programming - This work presents a novel analysis that allows to achieve tight complexity bounds of gradient-based methods for convex optimization. We start by identifying some of the...