US 2023/0274128 A1 · METHOD AND APPARATUS FOR ACCELERATED OPTIMIZATION

Abstract

A method, apparatus and system including the execution of an accelerated optimization method. According to an exemplary embodiment, the accelerated optimization method includes: first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is connected to the Hamiltonian of the optimal control problem via a zero-Hamiltonian, infinite-order, singular arc. The necessary conditions for the singular optimal control problem are used to produce an auxiliary controllable dynamical system whose trajectories generate algorithm primitives for the optimization problem. A three-step iterative map for a generic algorithm is designed by a semi-discretization step. Neither the feedback control law nor the differential equation governing the algorithm need be derived explicitly. A search direction is produced by a proximal-aiming-type method that dissipates a control Lyapunov function. New step size procedures based on minimizing control Lyapunov functions along a search vector complete the design of the accelerated optimization algorithms.

Claims20

Dependent claims

A method for processing digital representations of a group of objects and identifying within the group of objects a target object, the method including the execution of an accelerated optimization method to identify the target object within the digital representations of the group of objects, the accelerated optimization method comprising:

a) a user choosing a CLF V convergence condition;
b) initializing the accelerated optimization method according to:
λx0=−∂xL(1, λs0, x0), s0=e (x0) and setting k=0;
c) computing Vk=V(z(k));
d) while stopping conditions are not met do;
d1) generate ζ(k);
d2) compute hk0;
d3) advance to (z(k+1), x(k+1)) using hk0;
d4) compute Vk+1=V (z (k+1));
d5) while Vk+1 has not decreased sufficiently do;
d4a) backtrack (z(k+1), x(k+1)) along ζ(k);
recompute Vk+1;
d6) end while;
and
d7) update k←k+1;
and
e) end while.

14 more elements

A method for modeling a device or process to generate a model based on a group of digital representations of the device or process characteristics, the method including the execution of an accelerated optimization method to classify the digital representations of the device or process associated with each digital representation, the accelerated optimization method comprising:

a) a user choosing a CLF V convergence condition;
b) initializing the accelerated optimization method according to:
λx0=<∂xL(1, λs0, x0), s0=e(x0) and setting k=0;
c) computing Vk=V(z(k));
d) while stopping conditions are not met do;
d1) generate ζ(k);
d2) compute hk0;
d3) advance to (z(k+1), x(k+1)) using hk0;
d4) compute Vk+1=V(z(k+1));
d5) while Vk+1 has not decreased sufficiently do;
d4a) backtrack (z(k+1), x(k+1)) along ζ(k);
recompute Vk+1;
d6) end while;
and
d7) update k←k+1;
and
e) end while.

14 more elements

An apparatus for processing digital representations of a group of objects and identifying within the group of objects a target object, the apparatus including the execution of an accelerated optimization method to identify the target object within the digital representations of the group of objects , the accelerated optimization method comprising:

a) a user choosing a CLF V convergence condition;
b) initializing the accelerated optimization method according to:
λx0=−∂xL(1, λs0, x0), s0=e(x0) and setting k=0;
c) computing Vk=V(z(k));
d) while stopping conditions are not met do;
d1) generate ζ(k);
d2) compute hk0;
d3) advance to (z(k+1), x(k+1)) using hk0;
d4) compute Vk+1=V(z(k+1));
d5) while Vk+1 has not decreased sufficiently do;
d4a) backtrack (z(k+1), x(k+1)) along λ(k);
recompute Vk+1;
d6) end while;
and
d7) update k←k+1;
and
e) end while.

14 more elements

Dependencies are inferred from the claim text.

Method and apparatus for accelerated optimization

Life of this patent

Method and apparatus for accelerated optimization

Life of this patent

Abstract

Claims20