This paper describes a column generation algorithm for posynomial geometric programming which is based on Dantzig’s generalized linear programming principle. The algorithm works on the dual problem and avoids the traditional computational problems associated with dual-based algorithms. Test results indicate that the algorithm is extremely robust and can be used successfully to solve large-scale...

Linear programs are problems that involve the optimization of a linear objective function subject to linear constraints. Every linear program has an inherent geometric representation. Each constraint defines an halfspace and the feasible region of the the linear program is the convex polyhedron defined by intersection of all the halfspaces. The maximal solution to the linear program (if it exis...

The optimal solution of a geometric program (GP) can be sensitive to variations in the problem data. Robust geometric programming can systematically alleviate the sensitivity problem by explicitly incorporating a model of data uncertainty in a GP and optimizing for the worst-case scenario under this model. However, it is not known whether a general robust GP can be reformulated as a tractable o...

Convex Nonlinear Programming problems are all alike; every nonconvex problem is difficult in its own way. I am not the first numerical analyst to borrow the most quoted line of Anna Karenina to highlight the difficulties of non-linearity or non-convexity1. It could be argued that convex problems are not really “all alike”, but happy families are not either, therefore both the famous first sente...

A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solve even large-scale GPs extremely efficiently and reliably; at the same time a number of practical problems, particularly in circuit design, have been found to be equivalent to (or well approximated by) G...

This paper presents the programming language induced by the ordered structure of the Geometric Machine Model (GMM). The GMM is an abstract machine model, based on Girard’s coherence space, capable of modelling sequential, alternative, parallel (synchronous) and non-deterministic computations on a (possibly infinite) shared memory. The processes of the GMM are inductively constructed in a Cohere...

This study proposes a new multi-item inventory model with hybrid cost parameters under a fuzzy-stochastic constraint and permissible delay in payment. The price and marketing expenditure dependent stochastic demand and the demand dependent the unit production cost are considered. Shortages are allowed and partially backordered. The main objective of this paper is to determine selling price, mar...

The objective of this paper is to analyze entropy based Vendor Selection Problem (VSP) model by using fuzzy mathematical programming and primal-dual geometric programming method. Here we have extended the unconstrained convex programming approach to solve VSP model with inequality constraints without adding artificial variables. By t-norm based fuzzy mathematical programming technique and the d...