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Optimizing equational programs [chapter]

Robert Strandh
1987 Lecture Notes in Computer Science  
Equational programming [HO82b] involves replacing subterms in a term according to a set of equations or rewrite rules.  ...  Each time an equation is applied to the term, the subterm that matches the left hand side of the equation is replaced by the corresponding right hand side.  ...  As an application of our result, we discuss source-to-source transformations of an equational program E to an equational program F .  ... 
doi:10.1007/3-540-17220-3_2 fatcat:tjrjxy5cgvc7pbkui2xncuxuj4

Dynamic programming equation for the mean field optimal stopping problem [article]

Mehdi Talbi, Nizar Touzi, Jianfeng Zhang
2022 arXiv   pre-print
The effectiveness of our dynamic programming equation is illustrated by various examples including the mean-variance optimal stopping problem.  ...  The corresponding dynamic programming equation is an obstacle problem on the Wasserstein space, and is obtained by means of a general It\^o formula for flows of marginal laws of c\'adl\'ag semimartingales  ...  The corresponding dynamic programming equation is as usual derived by means of Itô's formula.  ... 
arXiv:2103.05736v2 fatcat:4kktjepiezebzn5kdskbyzmeni

Pansystems optimization, generalized principles of optimality, and fundamental equations of dynamic programming

Beifang Chen
1997 Kybernetes  
optimality which is equivalent to the fundamental recursive equation of dynamic programming.  ...  Fundamental equations of optimality Generalized dynamic programming Let ∆ and W be non-empty sets.  ... 
doi:10.1108/03684929710163209 fatcat:afmde7r7jfh3rehzcgcxb2n53a

Narrowing approximations as an optimization for equational logic programs [chapter]

María Alpuente, Moreno Falaschi, María José Ramis, Germán Vidal
1993 Lecture Notes in Computer Science  
Solving equations in equational theories is a relevant programming paradigm which integrates logic and equational programming into one unified framework.  ...  We also report on experimental results which demonstrate that our optimization can result in significant speed-ups in program execution.  ...  Our experiments indicate that the strategy can be a useful tool in the optimization of equational logic programs. first solution found termination achieved Goal basic refined basic refined cT g(h(s(0))  ... 
doi:10.1007/3-540-57186-8_93 fatcat:as5aukgkoza35gt7p3ppdpg53q

Lipschitz and Hölder stability of optimization problems and generalized equations

Helmut Gfrerer, Diethard Klatte
2015 Mathematical programming  
This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints.  ...  Furthermore, we apply the above results to parametric mathematical programs with equilibrium constraints and demonstrate, how some classical results for the nonlinear programming problem can be recovered  ...  Then, by duality theory of linear optimization, the dual program also has a solution v ∈ R n and ,ω) ).  ... 
doi:10.1007/s10107-015-0914-1 fatcat:owxx6iqicnahdd6dq6jw6aumn4

Mild solutions to the dynamic programming equation for stochastic optimal control problems [article]

Viorel Barbu, Chiara Benazzoli, Luca Di Persio
2017 arXiv   pre-print
We show via the nonlinear semigroup theory in L^1(R) that the 1-D dynamic programming equation associated with a stochastic optimal control problem with multiplicative noise has a unique mild solution  ...  programming equation (6) .  ...  The dynamic programming equation corresponding to the stochastic optimal control problem (1) is given by (see, e.g., [7] , [11] ),      ϕ t (t, x) + min u 1 2 σ 2 ϕ xx (t, x) u + H(u) +f (x) ϕ x  ... 
arXiv:1706.06824v1 fatcat:qd3jabbxynaotgbofdmuk2hb2a

Primal-dual bilinear programming solution of the absolute value equation

Olvi L. Mangasarian
2011 Optimization Letters  
We propose a finitely terminating primal-dual bilinear programming algorithm for the solution of the NP-hard absolute value equation (AVE): Ax − |x| = b, where A is an n × n square matrix.  ...  The algorithm, which makes no assumptions on AVE other than solvability, consists of a finite number of linear programs terminating at a solution of the AVE or at a stationary point of the bilinear program  ...  Bilinear Programming Algorithm for the Absolute Value Equation We begin by stating our bilinear algorithm as follows. Algorithm 3.1.  ... 
doi:10.1007/s11590-011-0347-6 fatcat:mjqzlic7wndv5k6mowk3knzxuy

Dynamic programming principle for delayed stochastic recursive optimal control problem and HJB equation with non-Lipschitz generator [article]

Jiaqiang Wen, Zhen Wu, Qi Zhang
2022 arXiv   pre-print
First, the dynamic programming principle for this control problem is obtained.  ...  solution of the associated Hamilton-Jacobi-Bellman equation.  ...  Tang-Zhang [27] obtained the dynamic programming principle in a pathdependent case and studied the associated path-dependent Bellman equations.  ... 
arXiv:2205.03052v2 fatcat:j42i66xeqfbybgb4rypisvrnii

Analysis And Optimization Of A Hybrid Linear Equation Solver Using Task-Based Parallel Programming Models

Claudia Rosas
2013 Zenodo  
This final step is accomplished by using the OmpSs task-based parallel programming language.  ...  This paper describes a methodology and tools to analyze and optimize the performance of task-based parallel applications.  ...  Tools and methodologies are necessary to efficiently optimize applications that follow a task-based parallel programming model.  ... 
doi:10.5281/zenodo.806944 fatcat:b73jpgqtdngy5ii5jibgelgw3u

Absolute Value Equation Solution Via Linear Programming

Olvi L. Mangasarian
2013 Journal of Optimization Theory and Applications  
By utilizing a dual complementarity property, we propose a new linear programming method for solving the NP-hard absolute value equation (AVE): The algorithm makes no assumptions on the AVE other than  ...  solvability and consists of solving a few linear programs, typically less than four.  ...  in the next section, where u is a dual optimal u of a previous linear programming iteration.  ... 
doi:10.1007/s10957-013-0461-y fatcat:qezmz7inkvc2hnsz4lcvzqrni4

Resolution and simplification of Dombi-fuzzy relational equations and latticized optimization programming on Dombi FREs [article]

Amin Ghodousian, Sara Zal
2022 arXiv   pre-print
It is proved that the algorithm can find the exact optimal solution and an example is presented to illustrate the proposed algorithm.  ...  In this paper, we introduce a type of latticized optimization problem whose objective function is the maximum component function and the feasible region is defined as a system of fuzzy relational equalities  ...  CONCLUSIONS Considering the practical applications of the max-Dombi fuzzy relational equations in FRE theory and that of the latticized programming, a nonlinear optimization problem was studied with the  ... 
arXiv:2207.07500v1 fatcat:dimw6as5urdi7b3tfvhrfgtqeu

Knapsack feasibility as an absolute value equation solvable by successive linear programming

O. L. Mangasarian
2008 Optimization Letters  
linear programs for solving the AVE.  ...  We formulate the NP-hard n-dimensional knapsack feasibility problem as an equivalent absolute value equation (AVE) in an n-dimensional noninteger real variable space and propose a finite succession of  ...  optimality condition for the quadratic program (6), points satisfying (27) have been very effective in solving nonconvex optimization problems such as those in [8, 7, 6] as well as our quadratic program  ... 
doi:10.1007/s11590-008-0102-9 fatcat:lfj4tb5wjzedvbc277hyupkccy

Sensitivity Analysis of Parametrized Programs via Generalized Equations

Alexander Shapiro
1994 SIAM Journal of Control and Optimization  
In this paper, we study sensitivity analysis of generalized equations (variational inequalities) with nonpolyhedral set constraints.  ...  This leads us to the introduction of an additional term representing a curvature of the constraint set in a linearization of the generalized equations.  ...  Unfortunately, it is not easy to extend the corresponding results from optimization problems to generalized equations (variational inequalities).  ... 
doi:10.1137/s0036139992230296 fatcat:fnkddwwybrhfvjv4hrp33utcbi

Dynamic programming principle for one kind of stochastic recursive optimal control problem and Hamilton-Jacobi-Bellman equations [article]

Zhen Wu, Zhiyong Yu
2007 arXiv   pre-print
equations.  ...  We will give the dynamic programming principle for this kind of optimal control problem and show that the value function is the unique viscosity solution of the obstacle problem for the corresponding Hamilton-Jacobi-Bellman  ...  Shige Peng for his elicitation and inspiring idea in recursive stochastic dynamic programming principle. The authors also thank Dr. Juan Li and Mingyu Xu for their helpful discussions and suggestions.  ... 
arXiv:0704.3775v1 fatcat:h4lgonsgdrcp7kiph4oxleh6pa

On the Dynamic Programming Approach for the 3D Navier–Stokes Equations

Luigi Manca
2007 Applied Mathematics and Optimization  
The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied.  ...  Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed.  ...  Then we shall justify the dynamic programming approach only for determinated classes of solution of the controlled equation, which depend on a given solution of the HJB equation.  ... 
doi:10.1007/s00245-007-9024-7 fatcat:pryjrsrjqzfs5lzewjz73telg4
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