CARMA OANT SEMINAR Speaker: Assoc Prof Regina Burachik, University of South Australia Title: An additive subfamily of enlargements of a maximally monotone Operator Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: SeeVogh (non-AG) [ENQUIRIES] Time and Date: 1:30 pm, Mon, 27th Apr 2015 Abstract: We introduce a subfamily of additive enlargements of a maximally monotone operator $T$. Our definition is inspired by the seminal work of Fitzpatrick presented in 1988. These enlargements are a subfamily of the family of enlargements introduced by Svaiter in 2000. For the case $T = \partial f$, we prove that some members of the subfamily are smaller than the $\varepsilon$-subdifferential enlargement. For this choice of $T$, we can construct a specific enlargement which coincides with the$\varepsilon$-subdifferential. Since these enlargements are all additive, they can be seen as structurally closer to the $\varepsilon$-subdifferential enlargement. Joint work with Juan Enrique Martínez-Legaz (Universitat Autonoma de Barcelona), Mahboubeh Rezaei (University of Isfahan, Iran), and Michel Théra (University of Limoges). [Permanent link] AMSI SUMMER SCHOOL LECTURE Speaker: Assoc Prof Regina Burachik, University of South Australia Title: Conjugate Duality for Optimization Location: Room GP201, General Purpose Building (Callaghan Campus) The University of Newcastle Dates: Wed, 21st Jan 2015 - Wed, 21st Jan 2015 Abstract: I will summarize the main ingredients and results on classical conjugate duality for optimization problems, as given by Rockafellar in 1973. [Permanent link] CARMA OANT SEMINAR Speaker: Assoc Prof Regina Burachik, University of South Australia Title: An additive subfamily of enlargements of a maximally monotone operator Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 10:00 am, Wed, 15th Oct 2014 Abstract: We introduce a subfamily of enlargements of a maximally monotone operator $T$. Our definition is inspired by a 1988 publication of Fitzpatrick. These enlargements are elements of the family of enlargements $\mathbb{E}(T)$ introduced by Svaiter in 2000. These new enlargements share with the $\epsilon$-subdifferential a special additivity property, and hence they can be seen as structurally closer to the $\epsilon$-subdifferential. For the case $T=\nabla f$, we prove that some members of the subfamily are smaller than the $\epsilon$-subdifferential enlargement. In this case, we construct a specific enlargement which coincides with the $\epsilon$-subdifferential. Joint work with Juan Enrique Martínez Legaz, Mahboubeh Rezaei, and Michel Théra. [Permanent link] CARMA OANT SEMINAR Speaker: Assoc Prof Regina Burachik, University of South Australia Title: Interior Epigraph Directions Method for Nonsmooth and Nonconvex Optimization via Generalized Augmented Lagrangian Duality Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 2:00 pm, Tue, 26th Nov 2013 Note earlier starting time. Abstract: We propose and study a new method, called the Interior Epigraph Directions (IED) method, for solving constrained nonsmooth and nonconvex optimization. The IED method considers the dual problem induced by a generalized augmented Lagrangian duality scheme, and obtains the primal solution by generating a sequence of iterates in the interior of the dual epigraph. First, a deflected subgradient (DSG) direction is used to generate a linear approximation to the dual problem. Second, this linear approximation is solved using a Newton-like step. This Newton-like step is inspired by the Nonsmooth Feasible Directions Algorithm (NFDA), recently proposed by Freire and co-workers for solving unconstrained, nonsmooth convex problems. We have modified the NFDA so that it takes advantage of the special structure of the epigraph of the dual function. We prove that all the accumulation points of the primal sequence generated by the IED method are solutions of the original problem. We carry out numerical experiments by using test problems from the literature. In particular, we study several instances of the Kissing Number Problem, previously solved by various approaches such as an augmented penalty method, the DSG method, as well as the popular differentiable solvers ALBOX (a predecessor of ALGENCAN), Ipopt and LANCELOT. Our experiments show that the quality of the solutions obtained by the IED method is comparable with (and sometimes favourable over) those obtained by the other solvers mentioned. Joint work with Wilhelm P. Freire and C. Yalcin Kaya. [Permanent link] CARMA OANT SEMINAR Speaker: Assoc Prof Regina Burachik, University of South Australia Title: Conditions for zero duality gap in convex programming Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle Access Grid Venue: UniSA Time and Date: 3:30 pm, Mon, 13th May 2013 Abstract: We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is weaker than all existing constraint qualifications, including the closed epigraph condition. Our dual condition was inspired by, and is weaker than, the so-called Bertsekas’ condition for monotropic programming problems. We give several corollaries of our result and special cases as applications. We pay special attention to the polyhedral and sublinear cases, and their implications in convex optimization. This research is a joint work with Jonathan M. Borwein and Liangjin Yao. [Permanent link]