MSThD43
Optimization algorithms and application  Part II of V
For Part I, see MSThBC43
For Part III, see MSThE43
For Part IV, see MSFrD43
For Part V, see MSFrE43
Date: August 13
Time: 13:3015:30
Room: 41
(Note: Click title to show the abstract.)
Organizer:
Wen, Zaiwen (Peking Univ.)
Yuan, Yaxiang (Inst. of Computational Mathematics & Scientific/Engineering Computing)
Xia, Yong (Beihang Univ.)
Abstract: This minisymposium consists 5 sessions. It highlights recent advances in theory, algorithms and applications of mathematical optimization on solving huge problems that are intractable for current methods.
MSThD431
13:3014:00
Sparse Tucker Tensor Representation for Multidimensional Seismic Data
Ma, Jianwei (Harbin Inst. of Tech.)
Abstract: Exploiting multidimensional sparsity structure of seismic data is important for seismic data processing and inversion. In this talk, we will apply a sparse Tucker tensor decompostion for multidimensional seismic data denoising and interpolation. Fast optimization methods will be applied for each dimension simultaneously to obain adaptive filters. We will compare the new method to previous datadriven tight frame (DDTF) method that first uses a vectorization step the highdimensional seismic data.
MSThD432
14:0014:30
The trace ratio problem
Zhang, Leihong (Shanghai Univ. of Finance & Economics)
Abstract: Maximizing the trace ratio over orthogonal constraints has a crucial role in pattern recognition. We shall discuss the characterization of the global optimal solutions of TRP and show the global and highorder convergence of an SCF iteration. We will explain why such SCF iteration is so efficient for TRP and also present perturbation analysis. Numerical experiments are reported and extension of TRP to maximize sum of two trace ratios will be also briefly discussed.
MSThD433
14:3015:00
Behavior analysis and greedy algorithm for optimal portfolio liquidation with market impact
XU, FFENGMIN (Xi'an Jiaotong Univ.)
Abstract: We analyze a nonconvex portfolio liquidation problem that maximize equity after trading subject to specified liability=equity requirements and box
constrains, with no restrictions on the relative magnitudes of permanent and temporary market impact. Through the intuition behind price factor, we naturally endow some important conclusions in Brown et al. (2010) and Chen et al. (2014) with new financial explanations. And the optimal state of this
nonconvex problem is revealed through the monotonicity of margin constraint
functions, in which the margin constraint is active and the equity and liability
after trading reaches the maximum at the same time. That is, it is just beyond
the ability to take the risk and holds the most available funds. Meanwhile, a
policy recommendation on determining an appropriate assetliability ratio is al
so given through the feasibility of portfolio liquidation. Further, we prove that
this problem is NPhard, and a greedy algorithm and its general convergence
are proposed. Numerical examples are presented to show the effectiveness of
the greedy algorithm compared to the Lagrangian algorithm in Chen et al.
(2014).
MSThD434
15:0015:30
Stochastic Compositional Gradient Descent: Algorithms for Minimizing Compositions of ExpectedValue Functions
Wang, Mengdi (Princeton Univ.)
Abstract: We focus on the minimization of a composition of two expectedvalue functions. In order to solve this stochastic composition problem, we propose a class of stochastic compositional gradient descent (SCGD) algorithms that can be viewed as stochastic versions of quasigradient method. The convergence involves the interplay of two iterations with different time scales.We prove that the almost sure convergence and different rates of convergence of SCGD under a variety of assumptions.
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Footnote: Code: TypeDateTimeRoom No.
Type : IL=Invited Lecture, SL=Special Lectures, MS=Minisymposia, IM=Industrial Minisymposia, CP=Contributed Papers, PP=Posters
Date: Mo=Monday, Tu=Tuesday, We=Wednesday, Th=Thursday, Fr=Friday
Time : A=8:309:30, B=10:0011:00, C=11:1012:10, BC=10:0012:10, D=13:3015:30, E=16:0018:00, F=19:0020:00, G=12:1013:30, H=15:3016:00
Room No.: TBA
