共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we consider a generalized semi-infinite optimization problem where the index set of the corresponding inequality constraints depends on the decision variables and the involved functions are assumed to be continuously differentiable. We derive first-order necessary optimality conditions for such problems by using bounds for the upper and lower directional derivatives of the corresponding optimal value function. In the case where the optimal value function is directly differentiable, we present first-order conditions based on the linearization of the given problem. Finally, we investigate necessary and sufficient first-order conditions by using the calculus of quasidifferentiable functions. 相似文献
2.
We consider a general convex stochastic control model. Our main interest concerns monotonicity results and bounds for the value functions and for optimal policies. In particular, we show how the value functions depend on the transition kernels and we present conditions for a lower bound of an optimal policy. Our approach is based on convex stochastic orderings of probability measures. We derive several interesting sufficient conditions of these ordering concepts, where we make also use of the Blackwell ordering. The structural results are illustrated by partially observed control models and Bayesian information models. 相似文献
3.
This paper considers the problem of maximizing expected
utility from consumption and terminal wealth under model uncertainty for a general
semimartingale market, where the agent with an initial capital and a random endowment
can invest. To find a solution to the investment problem we use the martingale method.
We first prove that under appropriate assumptions a unique solution to the investment
problem exists. Then we deduce that the value functions of primal problem and dual
problem are convex conjugate functions. Furthermore we consider a diffusion-jump-model
where the coefficients depend on the state of a Markov chain and the investor is
ambiguity to the intensity of the underlying Poisson process. Finally, for an agent
with the logarithmic utility function, we use the stochastic control method to derive
the Hamilton-Jacobi-Bellmann (HJB) equation. And the solution to this HJB equation can
be determined numerically. We also show how thereby the optimal investment strategy
can be computed. 相似文献
4.
This paper is devoted to the study of the first-order behavior of the value function of a parametric discrete optimal control problem with nonconvex cost functions and control constraints. By establishing an abstract result on the Mordukhovich subdifferential of the value function of a parametric mathematical programming problem, we derive a formula for computing the Mordukhovich subdifferential of the value function to a parametric discrete optimal control problem. 相似文献
5.
Patrick Mehlitz 《Optimization》2016,65(6):1203-1227
This article is dedicated to the study of bilevel optimal control problems equipped with a fully convex lower level of special structure. In order to construct necessary optimality conditions, we consider a general bilevel programming problem in Banach spaces possessing operator constraints, which is a generalization of the original bilevel optimal control problem. We derive necessary optimality conditions for the latter problem using the lower level optimal value function, ideas from DC-programming and partial penalization. Afterwards, we apply our results to the original optimal control problem to obtain necessary optimality conditions of Pontryagin-type. Along the way, we derive a handy formula, which might be used to compute the subdifferential of the optimal value function which corresponds to the lower level parametric optimal control problem. 相似文献
6.
M. Tamzali-Lafond 《Journal of Optimization Theory and Applications》2005,125(3):697-721
We consider an optimal control problem for a nonconvex control system under state constraints and the associated value function, which in general is not differentiable. We provide some characterizations of optimal trajectories using contingent derivatives. For this aim, we derive a costate satisfying the adjoint equation, the maximum principle, and a transversality condition linked to the superdifferential of the value function.Communicated by F. ZirilliThis paper is dedicated by the author to her children. 相似文献
7.
Huynh Van Ngai Nguyen Huu Tron Michel Théra 《Journal of Optimization Theory and Applications》2016,168(3):785-801
This paper studies the first-order behavior of the value function of a parametric optimal control problem with nonconvex cost functions and control constraints. By establishing an abstract result on the Fréchet subdifferential of the value function of a parametric minimization problem, we derive a formula for computing the Fréchet subdifferential of the value function to a parametric optimal control problem. The obtained results improve and extend some previous results. 相似文献
8.
Motivated by the study of parametric convex programs, we consider approximation of concave functions by piecewise affine functions.
Using dynamic programming, we derive a procedure for selecting the knots at which an oracle provides the function value and
one supergradient. The procedure is adaptive in that the choice of a knot is dependent on the choice of the previous knots.
It is also optimal in that the approximation error, in the integral sense, is minimized in the worst case.
This work was partially supported by NSERC (Canada) and FCAR (Québec). 相似文献
9.
E. N. Barron 《Journal of Optimization Theory and Applications》1983,41(4):573-586
We consider the minimization of the mean-square deviation of a prescribed function from the class of monotone functions. Two problems are considered. The first problem places no restriction on the initial value of the controls, while the second problem assumes that all the control functions must start at a fixed initial value. Optimal controls are exhibited in both problems. Finally, we consider the situation with general payoff and dynamics and give the heuristic characterization of the value function for such problems. 相似文献
10.
We consider an optimal impulse control problem on reinsurance, dividend and reinvestment of an insurance company. To close reality, we add fixed and proportional transaction costs to this problem. The value of the company is associated with expected present value of net dividends pay out minus the net reinvestment capitals until ruin time. We focus on non-cheap proportional reinsurance. We prove that the value function is a unique solution to associated Hamilton–Jacobi–Bellman equation, and establish the regularity property of the viscosity solution under a weak assumption. We solve the non-uniformly elliptic equation associated with the impulse control problem. Finally, we derive the value function and the optimal strategy of the control problem. 相似文献
11.
In this paper, we consider the compound Poisson risk model perturbed by diffusion with constant interest and a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generation function and the nth moment of the present value of all dividends until ruin are derived. We also derive integro-differential equations with boundary conditions for the Gerber-Shiu functions. The special case that the claim size distribution is exponential is considered in some detail. 相似文献
12.
J. O. Royset 《Mathematical Programming》2012,135(1-2):293-321
Optimality functions define stationarity in nonlinear programming, semi-infinite optimization, and optimal control in some sense. In this paper, we consider optimality functions for stochastic programs with nonlinear, possibly nonconvex, expected value objective and constraint functions. We show that an optimality function directly relates to the difference in function values at a candidate point and a local minimizer. We construct confidence intervals for the value of the optimality function at a candidate point and, hence, provide a quantitative measure of solution quality. Based on sample average approximations, we develop an algorithm for classes of stochastic programs that include CVaR-problems and utilize optimality functions to select sample sizes. 相似文献
13.
We consider the problem of constructing the convex envelope of a lower semi-continuous function defined over a compact convex set. We formulate the envelope representation problem as a convex optimization problem for functions whose generating sets consist of finitely many compact convex sets. In particular, we consider nonnegative functions that are products of convex and component-wise concave functions and derive closed-form expressions for the convex envelopes of a wide class of such functions. Several examples demonstrate that these envelopes reduce significantly the relaxation gaps of widely used factorable relaxation techniques. 相似文献
14.
In this article, we consider a portfolio optimization problem of the Merton’s type with complete memory over a finite time horizon. The problem is formulated as a stochastic control problem on a finite time horizon and the state evolves according to a process governed by a stochastic process with memory. The goal is to choose investment and consumption controls such that the total expected discounted utility is maximized. Under certain conditions, we derive the explicit solutions for the associated Hamilton–Jacobi–Bellman (HJB) equations in a finite-dimensional space for exponential, logarithmic, and power utility functions. For those utility functions, verification results are established to ensure that the solutions are equal to the value functions, and the optimal controls are also derived. 相似文献
15.
We consider a boundary control problem for the stationary convection–diffusion–reaction equation in which the reaction constant depends on the concentration of matter in such a way that the equation has a fifth-order nonlinearity. We prove the solvability of the boundary value problem and an extremal problem, derive an optimality system, and analyze it to derive estimates for the local stability of the solution of the extremal problem under small perturbations of both the performance functional and one of the given functions. 相似文献
16.
17.
We consider a mathematical model of a hybrid system in which the continuous dynamics generated at any point in time by one of a given finite family of continuous systems alternates with discrete operations commanding either an instantaneous switching from one system to another, or an instantaneous passage from current coordinates to some other coordinates, or both operations simultaneously. As a special case, we consider a model of a linear switching system. For a hybrid system, we introduce the notion of a weakly invariant set and analyze its structure. We obtain a representation of a weakly invariant set as a union of sets of simpler structure. For the latter sets, we introduce special value functions, for which we obtain expressions by methods of convex analysis. For the same functions, we derive equations of the Hamilton-Jacobi-Bellman type, which permit one to pass from the problem of constructing weakly invariant sets to the control synthesis problem for a hybrid system. 相似文献
18.
Utku Yildirim 《Operations Research Letters》2010,38(5):427-431
We investigate a problem of admission control in a queue with batch arrivals. We consider a single server with exponential service times and a compound Poisson arrival process. Each arriving batch computes its expected benefit and decides whether or not to enter the system. The controller’s problem is to set state dependent prices for arriving batches. Once prices have been set we formulate the admission control problem, derive properties of the value function, and obtain the optimal admission policy. 相似文献
19.
The classical Garman-Kohlhagen model for the currency exchange assumes that the domestic and foreign currency risk-free interest
rates are constant and the exchange rate follows a log-normal diffusion process.
In this paper we consider the general case, when exchange rate evolves according to arbitrary one-dimensional diffusion process
with local volatility that is the function of time and the current exchange rate and where the domestic and foreign currency
risk-free interest rates may be arbitrary continuous functions of time. First non-trivial problem we encounter in time-dependent
case is the continuity in time argument of the value function of the American put option and the regularity properties of
the optimal exercise boundary. We establish these properties based on systematic use of the monotonicity in volatility for
the value functions of the American as well as European options with convex payoffs together with the Dynamic Programming
Principle and we obtain certain type of comparison result for the value functions and corresponding exercise boundaries for
the American puts with different strikes, maturities and volatilities.
Starting from the latter fact that the optimal exercise boundary curve is left continuous with right-hand limits we give a
mathematically rigorous and transparent derivation of the significant early exercise premium representation for the value
function of the American foreign exchange put option as the sum of the European put option value function and the early exercise
premium.
The proof essentially relies on the particular property of the stochastic integral with respect to arbitrary continuous semimartingale
over the predictable subsets of its zeros. We derive from the latter the nonlinear integral equation for the optimal exercise
boundary which can be studied by numerical methods. 相似文献
20.
On the basis of the results of the first part of the paper, we consider necessary conditions for minimizing sequences in an
optimal control problem with a pointwise state constraint of inequality type and with dynamics described by a linear hyperbolic
equation in divergence form with the homogeneous Dirichlet boundary condition. The state constraint contains a function parameter
that belongs to the class of continuous functions and occurs as an additive term. For the parametric optimization problem,
we also consider regularity and normality conditions stipulated by the differential properties of its value function. 相似文献