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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some new algorithm developments on highly stiff stable schemes and on a SAV based approach for optimization problems
高刚性稳定方案 基于SAV 优化方法 新算法发展
2023/11/29
In the first part, I shall present a new way to construct highly stiff stable schemes. Traditional time discretization schemes are usually based on Taylor expansions at $t_{n+\beta}$ with $\beta\in [0...
Approximating the Expected Values for Combinatorial Optimization Problems over Stochastic Points
Approximating Expected Values Combinatorial Optimization Problems Stochastic Points
2016/1/22
We consider the stochastic geometry model where the location of each node is a random point in a given metric space,or the existence of each node is uncertain. We study the problem-s of computing the ...
A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems
A General Iterative Shrinkage Thresholding Algorithm Non-convex Regularized Optimization Problems
2013/5/2
Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterp...
On the Equivalence of Quadratic Optimization Problems Commonly Used in Portfolio Theory
investment analysis mean-variance analysis parameter uncertainty interval estimation test theory.
2012/9/14
In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e, the Markowitz mean-variance problem as well as the problems based on the mean-var...
Maximizing Expected Utility for Stochastic Combinatorial Optimization Problems
ExpectedStochastic CombinatorialProblems
2012/12/4
We study the stochastic versions of a broad class of combinatorial problems where the weights of the elements in the input dataset are uncertain. The class of problems that we study includes shortest ...
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...
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...
Belief Propagation Algorithm for Portfolio Optimization Problems
Belief Propagation Algorithm Portfolio Optimization Problems
2010/10/21
The typical behavior of optimal solutions to portfolio optimization problems with absolute deviation and expected shortfall models using replica analysis was pioneeringly estimated by S. Ciliberti and...
Transversality Conditions for Higher Order Infinite Horizon Discrete Time Optimization Problems
Transversality condition Dynamic optimization
2010/10/20
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...
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...
New Variants of Newton’s Method for Nonlinear Unconstrained Optimization Problems
unconstrained optimization Newton’s method order of convergence power means initial guess
2013/1/28
In this paper, we propose new variants of Newton’s method based on quadrature formula and power mean for solving nonlinear unconstrained optimization problems. It is proved that the order of convergen...
Making Robust Decisions in Discrete Optimization Problems as a Game against Nature
Discrete optimization minmax minmax regret game against nature
2009/7/17
In this paper a discrete optimization problem under uncertainty is discussed. Solving such a problem can be seen as a game against nature. In order to choose a solution, the minmax and minmax regret ...
IFS approximations of distribution functions and related optimization problems
iterated function systems optimization nonparametric statistics
2009/2/13
In this note an iterated function system (IFS) on the space of distribution functions
is built with the aim of proposing a new class of distribution function
estimators. One IFS estimator is propose...
Shape Optimization Problems over Classes of Convex Domains
Shape Optimization Problems Convex Domains
2009/2/5
We consider shape optimization problems of the form
\min\left\{\int_{\partial A} f(x,\nu(x))\hbox{d}x {\cal{H}^{n-1}} :A\in{\cal A}\right\}
where $f$ is any continuous function and the class ${\ca...
Optimization problems in designing automobiles
mathematical model optimization automobile design system approach
2010/11/1
A mathematical model of optimization problems in designing automobiles is suggested and requirements raised are defined taking into account the main technical and economic characteristics of the autom...