Hoang Tuy

Monotonic Optimization: Problems and Solution Approaches

Problems of maximizing or minimizing monotonic functions of n variables under monotonic constraints are discussed. A general framework for monotonic optimization is presented in which a key role is given to a property analogous to the separation property of convex sets. The approach is applicable to a wide class of optimization problems, including optimization problems dealing with functions representable as differences of increasing functions (d. i. functions).

Recent developments and trends in global optimization

Many optimization problems in engineering and science require solutions that are globally optimal. These optimization problems are characterized by the nonconvexity of the feasible domain or the objective function and may involve continuous and/or discrete variables. In this paper we highlight some recent results and discuss current research trends on deterministic and stochastic global optimization and global continuous approaches to discrete optimization.

D.C. Optimization: Theory, Methods and Algorithms

Optimization problems involving d.c. functions (differences of convex functions) and d.c. sets (differences of convex sets) occur quite frequently in operations research,economics, engineering design and other fields. We present a review of the theory, methods and algorithms for this class of global optimization problems which have been elaborated in recent years

Optimization on Low Rank Nonconvex Structures

Preface. Part I: Foundations. 1. Scope of Global Optimization. 2. Quasi-Convexity. 3. D.C. Functions and D.C. Sets. 4. Duality. 5. Low-Rank Nonconvex Structures. 6. Global Search Methods and Basic D.C. Optimization Algorithms. Part II: Methods and Algorithms. 7. Parametric Approaches in Global Optimization. 8. Multiplicative Programming Problems. 9. Monotonic Problems. 10. Decomposition Methods by Prices. 11. Dynamic Programming Algorithms in Global Optimization. Part III: Selected Applications. 12. Low Rank Nonconvex Quadratic Programming. 13. Continuous Location. 14. Design Centering and Related Geometric Problems. 15. Multiobjective and Bilevel Programming. References. Index.

Convergent Algorithms for Minimizing a Concave Function

For the problem of minimizing a concave function over a polytope a class of convergent algorithms is proposed, which is based upon a combination of the branch and bound technique with the cutting method developed earlier by H. Tuy.

Convex programs with an additional reverse convex constraint

AbstractA method is presented for solving a class of global optimization problems of the form (P): minimizef(x), subject tox∈D,g(x)≥0, whereD is a closed convex subset ofRn andf,g are convex finite functionsRn. Under suitable stability hypotheses, it is shown that a feasible point

A Conical Algorithm for Globally Minimizing a Concave Function Over a Closed Convex Set

\bar x

D.C. optimization approach to robust control: Feasibility problems

is optimal if and only if 0=max{g(x):x∈D,f(x)≤f(