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[CT167]

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : The VU-algorithm is a method of minimizing convex, nonsmooth functions by splitting the space into two subspaces: the V-space, on which the objective function's nonsmooth behavior is captured, and the orthogonal U-space, on which the function behaves smoothly. The algorithm's convergence is accelerated, as it takes a (slow) proximal point step in the V-space, then a (fast) quasi-Newton step in the U-space, since gradients and Hessians exist there. New convergence rates and subroutines are presented.
Classification : 90C25, 49J52
Author(s) :
- Chayne Planiden (University of Wollongong)

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : Proximal point algorithm (PPA) is an important class of methods for solving convex problems. In this article, a generalized multi-parameterized proximal point algorithm (GM-PPA) is developed to solve linearly constrained convex optimization problems. Compared with existing PPAs, the proposed method is much more general as well as flexible. Many existing PPAs reduce to our algorithm when some newly introduced parameters are fixed. Furthermore, by appropriately setting the algorithm parameters, our GM-PPA is potentially able to reduce the computation time and iteration number whereas the convergence result can still be guaranteed. Numerical experiments on synthetic problem are conducted to demonstrate the efficiency of our algorithm.
Classification : 90C25, 90C30
Author(s) :
- Yuan Shen ( Nanjing University of Finance & Economics)

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : In this talk I propose a proximal algorithm for minimizing an objective function of two block variables consisting of three terms: 1) a smooth function, 2) a nonsmooth function which is a composition between a strictly increasing, concave, differentiable function and a convex nonsmooth function, and 3) a smooth function which couples the two block variables. I propose a variable metric composite proximal alternating linearized minimization (CPALM) to solve this class of problems. Building on the powerful Kurdyka-\L ojasiewicz property, we derive the convergence analysis and establish that each bounded sequence generated by CPALM globally converges to a critical point. We demonstrate the CPALM method on parallel magnetic resonance image reconstruction problems. The obtained numerical results show the viability and effectiveness of the proposed method.
Classification : 90C26, 90C30, 49M37
Author(s) :
- Maryam Yashtini (Georgetown University)

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : In this work, we consider the difference of convex functions (DC) programming problems which are the backbone of nonconvex programming and global optimization. The classical problem contains the difference between two proper convex and lower semicontinuous functions. This paper deals with the generalized DC programming problem, which deals with the minimization of three convex functions. We propose a novel parametrized Douglas Rachford dynamical system to solve the problem and study its convergence behavior in the Hilbert space. Moreover, we also conduct numerical experiments to support our theoretical findings.
Classification : 90C26, 90C30
Author(s) :
- Avinash Dixit (Kirori Mal College, University of Delhi, Delhi)
- Pankaj Gautam (NTNU )
- Tanmoy Som (IIT (BHU), Varanasi)

Session Date & Time : 4D (Aug.24, 15:30-17:10)
Type : Contributed Talk
Abstract : The problem of distribution of blood has been extensively studied, but models relating to different blood types have not been specifically considered in the literature to the best of our knowledge. This paper describes a new mathematical model for optimising blood distribution in residential areas. A Lagrangian relaxation-based matheuristic is developed to solve the problem. Hypothetical data sets were generated to mimic real blood distribution system in an urban setting. Results obtained using CPLEX solver on the AMPL platform reveal that the model described in this study is able to achieve quality results within very short times. Specifically, the number of located blood facilities is minimized for each problem instances as well as covering much of the demand points on the distribution network. We observe that the proposed system, when compared to the existing system, provides a better approach to blood distribution and is adaptable to related areas of supply chain.
Classification : 90C26, 90C27
Author(s) :
- Olawale Joshua Adeleke (Redeemer's University )
- Olawale Joshua Adeleke (Redeemer's University)
- Idowu Ademola Osinuga (Federal University of Agriculture, Abeokuta, Nigeria)