Contributed Session Fri.3.H 0112

Friday, 15:15 - 16:45 h, Room: H 0112

Cluster 16: Nonlinear programming [...]

Optimality conditions II


Chair: Alexander Strekalovskiy



Friday, 15:15 - 15:40 h, Room: H 0112, Talk 1

Mourad Naffouti
On the second order optimality conditions for optimization problems with inequality constraints

Coauthors: Aderrahman Boukricha, Mabrouk Daldoul


A nonlinear optimization problem (P) with inequality constraints can be converted into a new optimization problem (PE) with equality constraints only. This is a Valentine method for
finite dimensional optimization. We review second order optimality conditions for (PE) in connection
with those of (P) and we give some new results.



Friday, 15:45 - 16:10 h, Room: H 0112, Talk 2

Alexander Strekalovskiy
New mathematical tools for new optimization problems


Following new paradigms of J.-S. Pang [Math. Program., Ser.B (2010) 125: 297-323] in mathematical optimization - competition, hierarchy and dynamics - we consider complementarity problems, bimatrix games, bilevel optimization problems etc, which turn out to be optimization problems with hidden nonconvexities.
However, classical optimization theory and method do not provide tools to escape stationary (critical, KKT) points produced by local search algorithms. As well-known, the conspicuous limitation of (classical) convex optimization methods applied to nonconvex problems is their ability of being trapped at a local extremum or even a critical point depending on a starting point. So, the nonconvexity, hidden or explicit, claims new mathematical tools allowing to reach a global solution through, say, a number of critical points.
In such a situation we advanced another approach the core of which is composed by global optimality conditions (GOC) for principal classes of d.c. programming problems. Furthermore, several special local search methods (SLSM) have been developed. Such an approach shows itself really efficient and allows to apply suitable package as X-Press, CPLEX etc.


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