on the minimal solutions of max min fuzzy relational equations in this paper the minimal solutions of max min fuzzy relational equations are investigated a sufficient and necessary condition for discriminating whether a given solution is minimal or not is shown furthermore we propose a new algorithm for computing all minimal solutions less than or equal to a given one

a note on a paper by e khorram and a ghodousian abstract the aim of this short note is to show on a numerical example that one of the two optimization algorithms proposed in e khorram a ghodousian linear objective function optimization with fuzzy relation equation constraints regarding max av composition appl math comput 173 2006 872 886 may not lead to the optimal solution in some cases besides it will be pointed out that the other algorithm correct but unfortunately ineffective for larger problems proposed in e khorram a ghodousian linear objective function optimization with fuzzy relation equation constraints regarding max av composition appl math comput 173 2006 872 886 can be extended to a wider class of non convex optimization problems

linear objective function optimization with fuzzy relation equation constraints regarding max av composition in this paper an optimization model with a linear objective function subject to a system of the fuzzy relation equations with max av composition is presented the solution set of such a fuzzy relation equations is a non convex set in this paper firstly we discuss the feasible solution set with two schemes and secondly study relationship between maximum and minimum points and also the feasible points as well furthermore an algorithm and few concrete examples are presented in order to optimize linear objective function

on the existence of weak solutions of nonlinear degenerate parabolic system with variable exponents abstract the main goal of the present paper is establishing the existence and uniqueness of weak solutions for the nonlinear degenerate reaction diffusion system with variable exponents a model also is proposed to characterize the invasion of cancer cells towards healthy cells with acidification environment moreover the main results of this paper are obtained using regularization problem the faedo galerkin approximation method some apriori estimates compactness results and the gronwall lemma

linear optimization with an arbitrary fuzzy relational inequality in this paper optimization of a linear objective function with fuzzy relational inequality constraints is investigated whereby an arbitrary function is considered as fuzzy composition the feasible solution set is determined and compared with some common results in the literature a necessary and sufficient condition and three other necessary conditions are presented to conceptualize the feasibility of the problem it is shown that in general a lower bound is always attainable for the optimal objective value moreover we prove that the optimal solution of the problem is obtained if the problem is defined by a non decreasing or non increasing function an algorithm is presented to summarize the process and an example is described to illustrate the algorithm

some results on the resolution of fuzzy relation equations abstract in this paper two special cases of the solution of the inverse problem are investigated the necessary and sufficient conditions for the existence of a solution such that the upper bound is the unit vector and for a unique solution of the inverse problem equal to the unit vector are presented an algorithmic approach which derives the output vector and the state matrix in each one of these cases is also proposed

minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations this paper considers the following optimization problem minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations using max product composition we first show some properties of minimal solutions of a system of fuzzy relation equations with max product composition and present some rules for reducing the original problem then we derive an algorithm which enables us to find all the optimal solutions for solving the optimization problem and provide some numerical examples to illustrate

solving a linear programming problem with the convex combination of the max min and the max average fuzzy relation equations abstract in this paper we introduce a fuzzy operator constructed by the convex combination of two known operators max min and max average compositions h j zimmermann fuzzy set theory and it s application kluwer academic publishers boston dordrecht london 1999 this operator contains some properties of the two known compositions when it generates the feasible region for linear optimization problems we investigate linear optimization problems whose feasible region is the fuzzy sets defined with this operator thus firstly the structure of these fuzzy regions is considered and then a method to solve the linear optimization problems with fuzzy equation constraints regarding this operator is presented

particle smoothing for hidden diffusion processes adaptive path integral smoother smoothing methods are used for inference of stochastic processes given noisy observations the estimation of the marginal posterior distribution given all observations is typically a computationally intensive task we propose a novel algorithm based on path integral control theory to efficiently estimate the smoothing distribution of continuous time diffusion processes from partial observations in particular we use an adaptive importance sampling method to improve the effective sampling size of the posterior and the reliability of the estimation of the marginals this is achieved by estimating a feedback controller together with an adaptive initialization and an annealing scheme to sample efficiently from the joint smoothing distribution we compare the results with estimations obtained from the standard forward filter backward simulator ffbsi for two diffusion processes of different complexity we show that the proposed method gives more accurate estimates than the standard ffbsi

relational equations in totally ordered lattices and their complete resolution abstract the set of all solutions of a composite fuzzy relation equation of sanchez inform and control 30 1976 defined on finite spaces is studied by determining and characterizing all the lower solutions of such an equation

convergence of max arithmetic mean powers of a fuzzy matrix fuzzy matrices provide convenient representations for fuzzy relations on finite universes in the literature the powers of a fuzzy matrix with max min max product max archimedean t norm compositions have been studied it turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved in this paper the max arithmetic mean composition is considered for the fuzzy relations we show that the max arithmetic mean powers of a fuzzy matrix always are convergent

minimizing a linear function under a fuzzy max min relational equation constraint in this paper we investigate the problem of minimizing a linear objective function subject to a fuzzy relational equation constraint a necessary condition for optimal solution is proposed based on this necessary condition we propose three rules to simplify the work of computing an optimal solution numerical examples are provided to illustrate the procedure experimental results are reported showing that our new procedure systematically outperforms our previous work

an algorithm for solving optimization problems with fuzzy relational inequality constraints an algorithm for solving a kind of optimization problems with fuzzy relational inequalities was proposed by guo and xia 6 however it is too expensive to verify the optimal condition in this paper some rules for reducing these problems are proposed and the relationship between minimal solutions and fri paths is also given these lead to a new algorithm for solving this kind of problems numerical experiments are presented for illustrating the efficiency of the proposed algorithm

solution algorithms for fuzzy relational equations with max product composition the conditions for the existence of an inverse solution to the max min composition of fuzzy relational equations have been well documented since the original work by sanchez 30 31 these same existence theorems have been extended to the t norm composition of relational equations in which the max product composition is a member 5 13 26 several studies 8 15 24 33 34 38 have shown that the max min operator may not always be the most desirable fuzzy relational composition and in fact the max product operator was superior in these instances this paper reviews the algorithms necessary to determine the complete solution of the inverse for fuzzy relational equations with max product composition

enhanced targeted sampling of high dimensional free energy landscapes using variationally enhanced sampling with an application to chignolin the capabilities of molecular simulations have been greatly extended by a number of widely used enhanced sampling methods that facilitate escaping from metastable states and crossing large barriers despite these developments there are still many problems which remain out of reach for these methods which has led to a vigorous effort in this area one of the most important problems that remains unsolved is sampling high dimensional free energy landscapes and systems that are not easily described by a small number of collective variables in this work we demonstrate a new way to compute free energy landscapes of high dimensionality based on the previously introduced variationally enhanced sampling and we apply it to the miniprotein chignolin

solving fuzzy relation equations with a linear objective function abstract an optimization model with a linear objective function subject to a system of fuzzy relation equations is presented due to the non convexity of its feasible domain defined by fuzzy relation equations designing an efficient solution procedure for solving such problems is not a trivial job in this paper we first characterize the feasible domain and then convert the problem to an equivalent problem involving 0 1 integer programming with a branch and bound solution technique after presenting our solution procedure a concrete example is included for illustration purpose

another modification from two papers of ghodousian and khorram and khorram et al abstract in this paper we focus on the proposed algorithms to solve a linear programming problem with the convex combination of the max min and the max average composition and the max star composition respectively they have been proposed by ghodousian and khorram a ghodousian e khorram solving a linear programming problem with the convex combination of the max min and the max average fuzzy relation equations appl math comput 180 2006 411 418 and khorram et al e khorram a ghodousian a abbasi molai solving linear optimization problems with max star composition equation constraints appl math comput 179 2006 654 661 respectively firstly we show that the tabular method algorithm in the first paper and the first procedure in the second paper may not lead to the optimal solutions of the two models in some cases secondly we generalize the proposed algorithm by abbasi molai and khorram a abbasi molai e khorram a modified algorithm for solving the proposed models by ghodousian and khorram and khorram and ghodousian appl math comput 190 2007 1161 1167 to solve the two models in fact it modifies the presented algorithms in the two papers finally some numerical examples are given to illustrate the purposes

optimization of fuzzy relational equations with max av composition max min and max product compositions are commonly utilized to optimize a linear objective function subject to fuzzy relational equations both are members in the class of max t norm composition in this study the max av composition is considered for the same optimization model which does not belong to the max t norm composition however max av composition generates some properties of the solution set that are similar to the max product composition thanks to these properties a simple value matrix with rules can be applied to reduce problem size thus this study proposes an efficient procedure for obtaining optimal solutions without decomposing the problem into two sub problems or finding all the potential minimal solutions

optimization of linear problems subjected to the intersection of two fuzzy relational inequalities defined by dubois prade family of t norms abstract in this paper optimization of a linear objective function with fuzzy relational inequality constraints is investigated in doing so the feasible region is formed by the intersection of two inequality fuzzy systems and dubois prade family of t norms which are considered as fuzzy composition the most well known continuous t norms are archimedean such as frank yager hamacher sugeno weber and schweizer sklar family an interesting family of t norms that is not archimedean has been introduced by dubois and prade in this paper the resolution of the feasible region of the problem is initialy investigated when it is defined with max duboise prade composition a necessary and sufficient condition along with three other necessary conditions are derived for determining the feasibility of the problem moreover two procedures have also been presented with the aim of simplifying the current linear problems a method is proposed to generate random feasible max dubois prade fuzzy relational inequalities and an algorithm is accordingly presented to solve the problem finally an example is described to illustrate this algorithm

rare event simulation of small noise diffusions an important sampling method for certain rare event problems involving small noise diffusions is proposed standard monte carlo schemes for these problems behave exponentially poorly in the small noise limit previous work in rare event simulation has focused on developing estimators with optimal exponential variance decay rates this criterion still allows for exponential growth of the statistical relative error we show that an estimator related to a deterministic control problem not only has an optimal variance decay rate but can have vanishingly small relative statistical error in the small noise limit the sampling method based on this estimator can be seen as the limit of the zero variance importance sampling scheme which uses the solution of the second order partial differential equation pde associated with the diffusion in the scheme proposed here this pde is replaced by a hamilton jacobi equation whose solution is computed pointwise on the fly from its variational formulation an operation that remains practical even in high dimensional problems we test the scheme on several simple illustrative examples as well as a stochastic pde the noisy allen cahn equation 2012 wiley periodicals inc

optimization of fuzzy relation equations with max product composition abstract an optimization problem with a linear objective function subject to a system of fuzzy relation equations using max product composition is considered since the feasible domain is non convex traditional linear programming methods cannot be applied we study this problem and capture some special characteristics of its feasible domain and the optimal solutions some procedures for reducing the original problem are presented the problem is transformed into a 0 1 integer program which is then solved by the branch and bound method for illustration purpose an example of the procedures is provided

an accelerated approach for solving fuzzy relation equations with a linear objective function in literature the optimization model with a linear objective function subject to fuzzy relation equations has been converted into a 0 1 integer programming problem by fang and li 1999 they proposed a jump tracking branch and bound method to solve this 0 1 integer programming problem in this paper we propose an upper bound for the optimal objective value based on this upper bound and rearranging the structure of the problem we present a backward jump tracking branch and bound scheme for solving this optimization problem a numerical example is provided to illustrate our scheme furthermore testing examples show that the performance of our scheme is superior to the procedure in the paper by fang and li several testing examples show that our initial upper bound is sharp

solution to the covering problem this work is motivated by recent investigations that reveal the intractability of the covering problem current methods for solving this problem lack an explicit procedure therefore they are of limited value this work presents the steps for solving such problems using a novel algorithm the search performance is better than that achieved in other works some numerical examples are presented to demonstrate the performance and to compare it with the performance of other methods the proposed algorithm can be utilized to solve fuzzy relation equations that exhibit the zero or greatest property

latticized linear optimization on the unit interval this paper considers the latticized linear optimization llo problem and its variants which are a special class of optimization problems constrained by fuzzy relational equations or inequalities we show that an optimal solution to such a problem can be obtained in polynomial time as long as the objective function is a max separable function with continuous monotone components we further show that the set of all optimal solutions is fully determined by one maximum optimal solution and a finite number of minimal optimal solutions the maximum optimal solution can be constructed in polynomial time once the optimal objective value is known while the detection of all minimal optimal solutions in an efficient manner remains as a challenging problem the relation between llo and max separable optimization and related issues are also investigated

coarse graining from variationally enhanced sampling applied to the ginzburg landau model a powerful way to deal with a complex system is to build a coarse grained model capable of catching its main physical features while being computationally affordable inevitably such coarse grained models introduce a set of phenomenological parameters which are often not easily deducible from the underlying atomistic system we present a unique approach to the calculation of these parameters based on the recently introduced variationally enhanced sampling method it allows us to obtain the parameters from atomistic simulations providing thus a direct connection between the microscopic and the mesoscopic scale the coarse grained model we consider is that of ginzburg landau valid around a second order critical point in particular we use it to describe a lennard jones fluid in the region close to the liquid vapor critical point the procedure is general and can be adapted to other coarse grained models

an algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max prod composition abstract fuzzy sets as the feasible region for optimization problems is an interesting and on going research topic s c fang g li solving fuzzy relations equations with a linear objective function fuzzy sets syst 103 1999 107 113 7 j lu s c fang solving nonlinear optimization problems with fuzzy relation constraints fuzzy sets syst 119 2001 1 20 16 e khorram a ghodpusian linear objective function optimization with fuzzy relation constraints regarding max av composition appl math comput in press doi 10 1016 j amc 2005 04 021 in this paper we focus on these kind problems in which the solutions region is the fuzzy relation equation with max prod composition and the objective function is linear whereas one of the major difficulties in such problems is non convexity of the feasible region it is preferable to study these regions in the first step hence we have primarily investigated two methods and their relationship and then we have determined the feasible region via them after determining the feasible set we have given an algorithm to optimize the linear objective function on such these regions finally we have presented two examples to illustrate the methods and algorithms

solving linear optimization problems with max star composition equation constraints in this paper an optimization model with a linear objective function subject to a system of fuzzy relation composition equations is presented since the non empty feasible solution set of the fuzzy relation equations is generally a non convex set the conventional linear programming method will not be suitable for solving such a problem therefore an efficient solution procedure for such problems appears to be necessary in this paper firstly we characterize the feasible solution set and then introduce two efficient procedures for solving the problem finally two concrete examples are included for more details

applications of the cross entropy method to importance sampling and optimal control of diffusions we study the cross entropy method for diffusions one of the results is a versatile cross entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems the approach is based on the minimization of a suitable cross entropy functional with a parametric family of exponentially tilted probability distributions we illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method

adaptive importance sampling for control and inference path integral pi control problems are a restricted class of non linear control problems that can be solved formally as a feynman kac pi and can be estimated using monte carlo sampling in this contribution we review pi control theory in the finite horizon case we subsequently focus on the problem how to compute and represent control solutions we review the most commonly used methods in robotics and control within the pi theory the question of how to compute becomes the question of importance sampling efficient importance samplers are state feedback controllers and the use of these requires an efficient representation learning and representing effective state feedback controllers for non linear stochastic control problems is a very challenging and largely unsolved problem we show how to learn and represent such controllers using ideas from the cross entropy method we derive a gradient descent method that allows to learn feed back controllers using an arbitrary parametrisation we refer to this method as the path integral cross entropy method or pice we illustrate this method for some simple examples the pi control methods can be used to estimate the posterior distribution in latent state models in neuroscience these problems arise when estimating connectivity from neural recording data using em we demonstrate the pi control method as an accurate alternative to particle filtering

evolution of a mathematical model of an aggressive invasive cancer under chemotherapy in this work we first propose continuous models of an aggressive invasive cancer which is characterized by its heterogeneity by its high proliferation rates and by the potential invasion of cancer cells into surrounding tissue an acidification environment mechanism is included in the models to analyze the level of invasion second we introduce and analyze their discrete versions obtained by an appropriate discretization afterwards a chemotherapy treatment with a gradual effect is added which includes important aspects as resistance and drug toxicity finally we make comparisons among different chemotherapy schemes to identify a suitable combination in order to eradicate or to reduce the growth of the tumor

on fuzzy relational equations and the covering problem previous studies have shown that fuzzy relational equations fres based on either the max continuous archimedean t norm or the max arithmetic mean composition can be transformed into the covering problem which is an np hard problem exploiting the properties common to the continuous archimedean t norm and the arithmetic mean this study proposes a generalization of them as the u norm enabling fres that are based on the max continuous u norm composition also to be transformed into the covering problem this study also proposes a procedure for transforming the covering problem into max product fres consequently max continuous u norm fres can be solved by extending any procedure for solving either the covering problem or max product fres

a nonstandard difference integral method for the viscous burgers equation abstract we develop a nonstandard difference integral method based on a nonstandard finite difference method coupled with a ce se scheme we use the viscous burgers equation with preestablished conditions as a benchmark for testing our method numerical results obtained show that this new method is more robust and efficient than the associated standard difference integral method

resolution of finite fuzzy relation equations abstract general schemes for solving fuzzy relation equations with finite sets are derived in this paper the relationship between the results derived here and those of previous publications regarding this subject is also discussed

importance sampling in path space for diffusion processes with slow fast variables importance sampling is a widely used technique to reduce the variance of a monte carlo estimator by an appropriate change of measure in this work we study importance sampling in the framework of diffusion process and consider the change of measure which is realized by adding a control force to the original dynamics for certain exponential type expectation the corresponding control force of the optimal change of measure leads to a zero variance estimator and is related to the solution of a hamilton jacobi bellmann equation we focus on certain diffusions with both slow and fast variables and the main result is that we obtain an upper bound of the relative error for the importance sampling estimators with control obtained from the limiting dynamics we demonstrate our approximation strategy with an illustrative numerical example

optimal control of molecular dynamics using markov state models a numerical scheme for solving high dimensional stochastic control problems on an infinite time horizon that appear relevant in the context of molecular dynamics is outlined the scheme rests on the interpretation of the corresponding hamilton jacobi bellman equation as a nonlinear eigenvalue problem that using a logarithmic transformation can be recast as a linear eigenvalue problem for which the principal eigenvalue and its eigenfunction are sought the latter can be computed efficiently by approximating the underlying stochastic process with a coarse grained markov state model for the dominant metastable sets we illustrate our method with two numerical examples one of which involves the task of maximizing the population of helices in an ensemble of small biomolecules alanine dipeptide and discuss the relation to the large deviation principle of donsker and varadhan

a modified algorithm for solving the proposed models by ghodousian and khorram and khorram and ghodousian abstract in this paper we focus on the proposed algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max prod composition that it has been proposed by ghodousian and khorram a ghodousian e khorram an algorithm for optimizing the linear function with fuzzy relation equation constraints regarding max prod composition appl math comput 178 2006 502 509 firstly we show that the algorithm may not lead to the optimal solution in some cases secondly we propose a new algorithm for solving the presented model by ghodousian and khorram 2006 as mentioned above in fact it modifies the presented algorithm in the ghodousian and khorram s paper also this algorithm is extended to the presented model by khorram and ghodousian e khorram a ghodousian linear objective function optimization with fuzzy relation equation constraints regarding max av composition appl math comput 173 2006 872 886 with max av composition finally some numerical examples are given for illustrating the purposes

solving nonlinear optimization problems with fuzzy relation equation constraints abstract an optimization model with a nonlinear objective function subject to a system of fuzzy relation equations is presented since the solution set of the fuzzy relation equations is in general a non convex set when it is not empty conventional nonlinear programming methods are not ideal for solving such a problem in this paper a genetic algorithm ga is proposed this ga is designed to be domain specific by taking advantage of the structure of the solution set of fuzzy relation equations the individuals from the initial population are chosen from the feasible solution set and are kept within the feasible region during the mutation and crossover operations the construction of test problems is also developed to evaluate the performance of the proposed algorithm

further contributions to the study of finite fuzzy relations equations abstract an interesting property of the schein rank of a fuzzy matrix stressed by k h kim and f w roush is formalized as definition of the basis of a set of fuzzy vectors defined over a commutative semiring with respect to another set of fuzzy vectors we apply this definition and another related concept in the setting of finite fuzzy relation equations in particular we give a sufficient condition for the existence of the smallest solution of a max min fuzzy equation

a linear programming approach for minimizing a linear function subject to fuzzy relational inequalities with addition min composition in this paper we study an optimization problem of minimizing a linear function subject to fuzzy relational inequalities with the addition min composition this optimization setting has recently been proposed to model the network cogestion issue when a bittorrent like peer to peer file sharing system is used for data transmission in a 2014 paper a pseudominimal index pmi based approach was proposed to search for an optimal solution it turns out that the pmi based approach may require to solve several to many linear programming problems in order to get an optimal solution in this paper we point out that the feasible domain is indeed convex and we only need to solve a single linear programming problem to generate an optimal solution for the original optimization problem furthermore our approach could be extended to the case with a nonlinear continuous objective function

linear optimization of bipolar fuzzy relational equations with max łukasiewicz composition according to the literature a linear optimization problem subjected to a system of bipolar fuzzy relational equations with max ukasiewicz composition can be translated into a 0 1 integer linear programming problem and solved using integer optimization techniques however the technique of integer optimization may involve hight computation complexity to improve computational efficiency for solving such an optimization problem this paper proves that each component of an optimal solution obtained from such an optimization problem can either be the corresponding component s lower bound or upper bound value because of this characteristic a simple value matrix with some simplified rules can be proposed to reduce the problem size first a simple solution procedure is then presented for determining optimal solutions without translating such an optimization problem into a 0 1 integer linear programming problem two examples are provided to illustrate the simplicity and efficiency of the proposed algorithm

a note on a paper by molai and khorram abstract the aim of this note is to show that the optimization algorithm proposed in 6 may not lead to the optimal solution in some cases in fact the optimization problem remains open if we do not apply the branch and bound method to solve it or compute all the objective values of minimal solutions of the feasible domain

fuzzy relation equations on a finite set abstract the family of all the solutions of a fuzzy relation equation on a finite set is considered it is characterized by the set of all the lower solutions which can be obtained by a combinatorial algorithm

a modified pso algorithm for linear optimization problem subject to the generalized fuzzy relational inequalities with fuzzy constraints fri fc in this paper optimization of a linear objective function subject to a generalized fuzzy relational inequalities is investigated in which an arbitrary continuous t norm is considered as fuzzy composition and fuzzy inequality replaces ordinary inequality in the constraints unlike most optimization algorithms in fuzzy relational inequalities with fuzzy constraints fri fc we find a near feasible solution having a better objective value than those resulting from the resolution of the similar problems with crisp ordinary inequality constraints such solutions are called super optima in this paper subsequently an algorithm is proposed to find a super optimum with pre specified desirable infeasibility for this purpose we firstly study some structural properties of the fri fc problem and present a new formulization that is independent of t norms used in the constraints of the problem this new formulation converts the primary problem into an equivalent problem with simple constraints without considering any penalty parameters however it is proved that the transformed equivalent problem enables our algorithm to distinguish unfavorable points and generate a sequence of solutions converging to a super optimum under a certain sufficient condition finally a modified pso is presented in which the ability of pso to solve unconstrained problems with continuous domain the structure of the transformed problem and some fuzzy structural modifications are combined and form an efficient algorithm to solve the generalized fri fc problems the modified pso algorithm has been applied to the generalized fri fc problem defined with ten well known continuous t norms additionally an idea of the fri fc problems as outer approximators for fri problems with ordinary inequalities is also investigated

posynomial geometric programming problem subject to max min fuzzy relation equations we discuss a class of posynomial geometric programming problem pgpf aimed at minimizing a posynomial subject to fuzzy relational equations with max min composition by introducing auxiliary variables we convert the pgpf into an equivalent programming problem whose objective function is a non decreasing function with an auxiliary variable we show that an optimal solution consists of a maximum feasible solution and one of the minimal feasible solutions by an equivalent programming problem in addition we introduce some rules for simplifying the problem then by using a branch and bound method and fuzzy relational equations fre path we present an algorithm to obtain an optimal solution to the pgpf finally numerical examples are provided to illustrate the steps of the procedure