## Contributed Session Thu.1.H 0112

#### Thursday, 10:30 - 12:00 h, Room: H 0112

**Cluster 16: Nonlinear programming** [...]

### Convex nonlinear optimization I

**Chair: Ganesh Perumal**

**Thursday, 10:30 - 10:55 h, Room: H 0112, Talk 1**

**Stefan M. Stefanov**

Convex separable minimization with box constraints

**Abstract:**

Consider minimization problems with a convex separable objective function subject to a convex separable inequality constraint of the form "less than or equal to'' / linear equality constraint / linear inequality constraint of the form "greater than or equal to'', respectively, and bounds on the variables (box constraints). Such problems arise in both theoretical considerations and in practical problems. For the first and the second problem, a necessary and sufficient condition is proved for a feasible solution to be an optimal solution to the respective problem, and a sufficient condition is proved for a feasible solution to be an optimal solution to the third problem. Algorithms of polynomial computational complexity for solving these three problems are proposed and convergence of algorithms is proved. Some particular problems of the form under consideration as well as numerical results are presented.

**Thursday, 11:00 - 11:25 h, Room: H 0112, Talk 2**

**Ganesh Perumal**

A decomposition technique for convex optimization problems

**Coauthor: G. N. Srinivasa Prasanna**

**Abstract:**

In this presentation, we give a decomposition technique that is applicable to general convex optimization problems. The feasible space is divided into small sub-spaces and information about a particular sub-space containing the optimal solution is estimated from the cost function and the constraint set. The properties of such sub-spaces and their existential proof are explained. The complexity of applying this decomposition technique is also discussed.