The main contributions in this thesis are advances in parametric programming. The thesis is divided into two parts; theoretical advances and application areas for parametric programming. The first part deals with continuity properties and the structure of solutions to convex parametric quadratic and linear programs. The second part focuses on applications of parametric quadratic and linear prog...

It has been shown by Fiacco that convexity or concavity of the optimal value of a parametric nonlinear programming problem can readily be exploited to calculate global parametric upper and lower bounds on the optimal value function. The approach is attractive because it involves manipulation of information normally required to characterize solution optimality. We briefly describe a procedure fo...

Bilevel optimization problems with multivalued objective functions in both levels are first replaced by a problem with a parametric lower level using a convex combination of the lower level objectives. Thus a nonconvex multiobjective bilevel optimization problem arises which is then transformed into a parametric bilevel programming problem. The investigated problem has been considered in the pa...

We introduce a class of “inverse parametric optimization” problems, in which one is given both a parametric optimization problem and a desired optimal solution; the task is to determine parameter values that lead to the given solution. We describe algorithms for solving such problems for minimum spanning trees, shortest paths, and other “optimal subgraph” problems, and discuss applications in m...

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lipschitz and upper Hölder type, respectively, hold. Furthermore, we apply the ...

Topological design of terrestrial networks for communication via satellites is studied in the paper. Quantitative model of the network cost-analysis minimizing the total transmission and switching cost is described. Several algorithms solving combinatorial problem of the optimal topology design based on binary partitioning, a minimax parametric search and dynamic programming are developed by th...

We introduced and discussed a second-ordered parametric dual model of complex multi-objective programming problem (P). Moreover, the authors constructed proved weak, strong strictly converse duality theorems by generalized Θ-bonvexity.

A parametric meshing technique is presented with special emphasis to singularities in the parametric mapping. Singularities are locations where the parametric mapping is highly distorted or even singular. In a NURBS context, this arises when control points are clustered into the same location in three dimensions. Limitations of parametric plane meshing in this context are highlighted, and zeroa...

This chapter presents a suite of systems we developed that constitute a solution for bringing programming to end users in the field of computeraided design (CAD), by using programming by demonstration (PBD). This suite includes the LIKE system, which laid the foundations of our method, and the EBP system (Example Based Programming in Parametrics), which is intended to enable CAD system users to...

In this paper, a new concept of the fuzzy stability set of the first kind for multi-level multi-objective fractional programming (ML-MOFP) problems having a single-scalar parameter in the objective functions and fuzziness in the right-hand side of the constraints has been introduced. Firstly, A parametric ML-MOFP model with crisp set of constraints is established based on the -cut approach. Sec...