A convex programming problem in Banach spaces and applications to optimum control theory (original) (raw)

An existence theorem for an optimal control problem in banach spaces

Bulletin of the Australian Mathematical Society, 1989

In this paper we prove the existence of an optimal admissible state-control pair for a nonlinear distributed parameter system, with control constraints of feedback type and with an integral cost criterion. An example is also worked in detail.

Existence for minimization in Banach space with some applications

Existence of a minimum is shown for a coercive, kc differentiable function restricted to a finite intersection of half spaces under a structural assumption on the GLteaux derivative. This abstract existence result is illustrated by two examples from optimal control theory for distributed systems. 7'

Existence Theorem for Deterministic Optimal Control Problems

La Matematica

In this paper, we give a general formulation of a deterministic Optimal Control Problem (OCP) and we transform it in an optimization problem of the form min x∈S J (x), where S is a nonempty subset of a Banach space and J a continuous functional defined on S. It is well known according to the Weierstrass theorem that the optimization problem (see above equation) has a solution when S is a compact set and J is a continuous function. Given that the considered set S in our problem of study is noncompact, we consider a weakly* version of the Weierstrass theorem by showing that S is sequentially weakly* compact and J is sequentially weakly* lower semicontinuous. This allows us to obtain a useful existence theorem which gives sufficient conditions B Eric Kokomo

The Lagrange Multipliers for Convex Vector Functions in Banach Spaces

2018

This paper is devoted to vector-valued optimization problems in Banach spaces whose objective functions are cone-convex and the feasible sets are not assumed to be convex. By means of a well-known nonlinear scalarizing function and the oriented distance function, we derive optimality conditions for weak Pareto solutions and (; e)-Pareto solutions in terms of abstract subdierentials and the Clarke subdierential. KEYWORDS: Lagrange multiplier, cone-convex function, Lipschitz function, (weak) Pareto min- imal point, (; e)-Pareto minimal point, nonlinear scalarizing functional, oriented distance function, subdierential. MSC: 46A40, 49J53, 52A41, 90C30, 90C46.

Lagrangian conditions for vector optimization in Banach spaces

Mathematical Methods of Operations Research, 2006

We consider vector optimization problems on Banach spaces without convexity assumptions. Under the assumption that the objective function is locally Lipschitz we derive Lagrangian necessary conditions on the basis of Mordukhovich subdifferential and the approximate subdifferential by Ioffe using a non-convex scalarization scheme. Finally, we apply the results for deriving necessary conditions for weakly efficient solutions of nonconvex location problems.

Convexity and optimization in banach spaces

Acta Applicandae Mathematicae, 1991

Cinii-convexity and optimization in banach Convexity and optimization in Banach spaces. Viorel Barbu, Teodor Precupanu Springer monographs in mathematics Springer, c2012. 4th ed Eeor e6616: convex optimization-columbia EEOR E6616: Convex Optimization Convex Optimization in Banach Spaces. Convex Optimization by Boyd and Vandenberghe and detailed Convexity and optimization in banach spaces Convexity and Optimization in Banach Spaces CONVEXITY & OPTIMIZATION IN BA Springer Monographs in Mathematics Teodor Precupanu; SPRINGER VERLAG GMBH; Convexity and optimization in banach spaces-Convexity and optimization in banach spaces [1401.0334] convex optimization on banach spaces Dec 31, 2013 Convex optimization on Banach Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach Convexity and optimization in banach spaces-Convexity and Optimization in Banach Spaces. , Prof.