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...

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...

Abstract Conditional Sums-of-AM/GM-Exponentials (conditional SAGE) is a decomposition method to prove nonnegativity of signomial or polynomial over some subset X real space. In this article, we undertake the first structural analysis conditional SAGE signomials for convex sets . We introduce -circuits finite $${\mathcal {A}}\subset {\mathbb {R}}^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/M...

In this article, we propose a geometric programming method in order to compute lower bounds for real polynomials. We provide new sufficient conditions for polynomials to be nonnegative as well as to have a sum of binomial squares representation. These criteria rely on the coefficients and the support of a polynomial and generalize all previous ones by Lasserre, Ghasemi, Marshall, Fidalgo and Ko...

Certifying function nonnegativity is a ubiquitous problem in computational mathematics, with especially notable applications optimization. We study the question of certifying signomials based on recently proposed approach Sums-of-AM/GM-Exponentials (SAGE) decomposition due to second author and Shah. The existence SAGE sufficient condition for signomial, it can be verified by solving tractable c...

A credal network associates sets of probability distributions with directed acyclic graphs. Under strong independence assumptions, inference with credal networks is equivalent to a signomial program under linear constraints, a problem that is NP-hard even for categorical variables and polytree models. We describe an approach for inference with polytrees that is based on branch-and-bound optimiz...

Signomial programs (SPs) are optimization problems specified in terms of signomials, which are weighted sums of exponentials composed with linear functionals of a decision variable. SPs are non-convex optimization problems in general, and families of NP-hard problems can be reduced to SPs. In this paper we describe a hierarchy of convex relaxations to obtain successively tighter lower bounds of...

This paper presents the application of geometric programming for combined high-level and low-level architecture parameter exploration. This paper builds an geometric programming framework for reconfigurable architectures, and presents a full delay and area model of an FPGA. This optimization allows high-level architectural parameter selection and the transistor sizing to be done concurrently. T...

We trace progress and thinking about the Strominger-Yau-Zaslow conjecture since its introduction in 1996. In particular, we aim to explain how the conjecture led to the algebro-geometric program developed by myself and Siebert, whose objective is to explain mirror symmetry by studying degenerations of Calabi-Yau manifolds. We end by outlining how tropical curves arise in the mirror symmetry story.