Fritz John Type Duality in Nondifferentiable Continuous Programming with Equality and Inequality Constraints

A Fritz John type dual for a nondifferentiable continuous programming problem with equality and inequality constraints which represent many realistic situations is formulated using Fritz John type optimality conditions instead of Karush-Kuhn-Tucker type conditions and thus does not require a regularity condition. Various duality results under suitable generalized convexity assumptions are derived. A pair of Fritz John type dual continuous programming with natural boundary conditions rather than fixed end points is also presented. Finally, it is pointed that our duality results can be considered as dynamic generalizations of those of a nondifferentiable nonlinear programming problem in the presence of equality and inequality constraints recently treated in the literature

Convex function and optimization techniques

Optimization is the process of maximizing or minimizing a desired objective function while satisfying the prevailing constraints. The optimization problems have two major divisions. One is linear programming problem and other is non-linear programming problem. But the modern game theory, dynamic programming problem, integer programming problem also part of the Optimization theory having wide range of application in modern science, economics and management. In the present work I tried to compare the solution of Mathematical programming problem by Graphical solution method and others as well as its theoretic descriptions. As we know that not like linear programming problem where multidimensional problems have a great deal of applications, non-linear programming problem mostly considered only in two variables. Therefore for nonlinear programming problems we have an opportunity to plot the graph in two dimensions and get a concrete graph of the solution space which will be a step ahead in its solutions. Nonlinear programming deals with the problem of optimizing an objective function in the presence of equality and inequality constraints. The development of highly efficient and robust algorithms and software for linear programming, the advent of high speed computers, and the education of managers and practitioners in regard to the advantages and profitability of mathematical modeling and analysis, have made linear programming an important tool for solving problems in diverse fields. However, many realistic problems cannot be adequately represented or approximated as a linear program owing to the nature of the nonlinearity of the objective function or the nonlinearity of any of the constraints

Evaluating probabilistic programming languages for simulating quantum correlations

This article explores how probabilistic programming can be used to simulate quantum correlations in an EPR experimental setting. Probabilistic programs are based on standard probability which cannot produce quantum correlations. In order to address this limitation, a hypergraph formalism was programmed which both expresses the measurement contexts of the EPR experimental design as well as associated constraints. Four contemporary open source probabilistic programming frameworks were used to simulate an EPR experiment in order to shed light on their relative effectiveness from both qualitative and quantitative dimensions. We found that all four probabilistic languages successfully simulated quantum correlations. Detailed analysis revealed that no language was clearly superior across all dimensions, however, the comparison does highlight aspects that can be considered when using probabilistic programs to simulate experiments in quantum physics.Comment: 24 pages, 8 figures, code is available at https://github.com/askoj/bell-ppl