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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Capsule Aggregated Attention for Vehicle Routing Problems
车辆 路径问题 胶囊聚合 关注
2023/4/27
Deep learning based methods have shown great potential for solving Vehicle Routing Problems (VRPs) in recent years. In the current learning based models, attention mechanism plays an important role an...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse Problems on Piezoelectric Equations
压电方程 反问题 狄利克雷 诺依曼映射 有限子域
2023/4/26
In this talk, recent progress on inverse problems for piezoelectric equations is discussed. We show a uniqueness result on recovering coefficients of piecewise homogeneous piezoelectric equations from...
A primal-dual potential reduction method for problems involving matrix inequalities
Interior point algorithms Linear matrix inequaliües Semidefinite programming
2015/8/11
We describe a potential reduction method for convex optimization problems involving matrix inequalities. The method is based on the theory developed by Nesterov and Nemirovsky and generalizes Gonzaga ...
Semidefinite programming relaxations of non-convex problems in control and combinatorial optimization
Applications of semidefinite programming combinatorial optimization quadratic semi-definite programming bilinear matrix inequality
2015/8/11
We point out some connections between applications of semidefinite programming in control and in combinatorial optimization. In both fields semidefinite programs arise as convex relaxations of NP-hard...
Time-Inconsistent Optimal Control Problems and the Equilibrium HJB Equation
time-inconsistent optimal control problem equilibrium value function equilibrium Hamilton Jacobi-Bellman equation
2012/4/18
A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equat...
Sequential Convex Programming Methods for Solving Nonlinear Optimization Problems with DC constraints
Sequential convex programming DC constraint relaxation technique nonconvex optimization
2011/9/22
Abstract: This paper investigates the relation between sequential convex programming (SCP) as, e.g., defined in [24] and DC (difference of two convex functions) programming. We first present an SCP al...
Carleman Estimate for Stochastic Parabolic Equations and Inverse Stochastic Parabolic Problems
Stochastic parabolic equations Carleman estimate conditional stability inverse source problem
2011/9/22
Abstract: In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we solve two inverse problems for stochastic parabolic equations. One is co...
A One-Dimensional Local Tuning Algorithm for Solving GO Problems with Partially Defined Constraints
Global optimization multiextremal constraints geometric algorithms index scheme local tuning
2011/9/21
Abstract: Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this p...
Tchebycheff systems and extremal problems for generalized moments: a brief survey
Tchebycheff systems extremal problems brief survey Optimization and Control
2011/9/14
Abstract: A brief presentation of basics of the theory of Tchebycheff and Markov systems of functions and its applications to extremal problems for integrals of such functions is given. The results, a...
The power quantum calculus and variational problems
Quantum variational problems n q-power difference operator generalized Norlund sum
2011/8/23
Abstract: We introduce the power difference calculus based on the operator $D_{n,q} f(t) = \frac{f(qt^n)-f(t)}{qt^n -t}$, where $n$ is an odd positive integer and $0Properties of the new operat...
Unsolved Problems in Visibility Graphs of Points, Segments and Polygons
Unsolved Problems Visibility Graphs of Points Segments Polygons
2011/3/3
In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.
Explicit Solutions to Boundary Problems for 2+1-Dimensional Integrable Systems
Explicit Solutions to Boundary Problems 2+1-Dimensional Integrable Systems
2010/12/28
Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for bou...
Spectral Optimization Problems
optimization problems for eigenvalues shape optimization capacity
2011/2/21
In this survey paper we present a class of shape optimization problems where the cost function involves the solution of a PDE of elliptic type in the unknown domain.In particular, we consider cost fun...
Transversality Conditions for Higher Order Infinite Horizon Discrete Time Optimization Problems
Transversality condition Dynamic optimiza-tion Infinite horizon Higher order difference problems
2010/4/28
In this paper, we examine higher order difference problems. Using the "squeezing" argument, we derive both Euler's condition and the transversality condition. In order to derive the two conditions, tw...
Solving Fuzzy Linear Programming Problems with Linear Membership Function
Fuzzy linear programming fuzzy number modified subgradient method fuzzy decisive set method
2010/3/1
In this paper, we concentrate on two kinds of fuzzy linear programming problems: linear programming problems with only fuzzy technological coefficients and linear programming problems in which both th...