Hector Ramirez Cabrera

• Docteur en Mathématiques Appliquées, École Polytechnique, Palaisseu, France
• Professor (Full) at University of Chile

The constraint nondegeneracy condition is one of the most relevant and useful constraint qualifications in nonlinear semidefinite programming. It can be characterized in terms of any fixed orthonormal basis of the, let us say, \(\ell \)-dimensional kernel of the constraint matrix, by the linear independence of a set of \(\ell (\ell +1)/2\) derivati...

In a previous paper [R. Andreani, G. Haeser, L. M. Mito, H. Ram\'irez, T. P. Silveira. First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition. Mathematical Programming, 2023. DOI: 10.1007/s10107-023-01942-8] we introduced a constant rank constraint qualification for nonlinear...

This work tackles the open pit planning problem in an optimal control framework. We study the optimality conditions for the so-called continuous formulation using Pontryagin’s Maximum Principle, and introduce a new, semi-continuous formulation that can handle the optimization of a two-dimensional mine profile. Numerical simulations are provided for...

The well known constant rank constraint qualification [Math. Program. Study 21:110–126, 1984] introduced by Janin for nonlinear programming has been recently extended to a conic context by exploiting the eigenvector structure of the problem. In this paper we propose a more general and geometric approach for defining a new extension of this conditio...

We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an application of these conditions, we provide a unified global convergence proof of a class of algorithms to stationary points without assuming neither uniqueness of the Lagr...

We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state...

In Andreani et al. (Weak notions of nondegeneracy in nonlinear semidefinite programming, 2020), the classical notion of nondegeneracy (or transversality) and Robinson’s constraint qualification have been revisited in the context of nonlinear semidefinite programming exploiting the structure of the problem, namely its eigendecomposition. This allows...

In this note we show with a counter-example that all conditions proposed in Zhang and Zhang (Set-Valued Var. Anal 27:693–712 2019) are not constraint qualifications for second-order cone programming.

The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first- and second-order algorithms, and for computing the directional derivative of the value function. In this paper we discuss naive extensions of constant rank-type constrain...

We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with constraint, and another one in terms of a differential inclusion with upper-semi continuous right member but without constrai...

In [R. Andreani, G. Haeser, L. M. Mito, H. Ram\'irez C., Weak notions of nondegeneracy in nonlinear semidefinite programming, arXiv:2012.14810, 2020] the classical notion of nondegeneracy (or transversality) and Robinson's constraint qualification have been revisited in the context of nonlinear semidefinite programming exploiting the structure of t...

Nonpharmaceutical interventions (NPI) such as banning public events or instituting lockdowns have been widely applied around the world to control the current COVID-19 pandemic. Typically, this type of intervention is imposed when an epidemiological indicator in a given population exceeds a certain threshold. Then, the nonpharmaceutical intervention...

The well known constant rank constraint qualification [Math. Program. Study 21:110-126, 1984] introduced by Janin for nonlinear programming has been recently extended to a conic context by exploiting the eigenvector structure of the problem. In this paper we propose a more general and geometric approach for defining a new extension of this conditio...

We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an application of these conditions, we provide a unified global convergence proof of a class of algorithms to stationary points without assuming neither uniqueness of the Lagr...

This article deals with the inclusion of microbial ecology measurements such as abundances of operational taxonomic units in bioprocess modelling. The first part presents the mathematical analysis of a model that may be framed within the class of Lotka–Volterra models fitted to experimental data in a chemostat setting where a nitrification process...

Background Syphilis, together with other sexually transmitted infections, remains a global public health problem that is far from controlled. People deprived of liberty are a vulnerable population. Control activities in prisons rely mostly on passive case detection, despite the existence of affordable alternatives that would allow switching to acti...

The constraint nondegeneracy condition is one of the most relevant and useful constraint qualifications in nonlinear semidefinite programming. It can be characterized in terms of any fixed orthonormal basis of the, let us say, $\ell$-dimensional kernel of the constraint matrix, by the linear independence of a set of $\ell(\ell+1)/2$ derivative vect...

Nonpharmaceutical interventions (NPI) such as banning public events or instituting lockdowns have been widely applied around the world to control the current COVID-19 pandemic. Typically, this type of intervention is imposed when an epidemiological indicator in a given population exceeds a certain threshold. Then, the nonpharmaceutical intervention...

The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first-and second-order algorithms, and for computing the derivative of the value function. In this paper we discuss naive extensions of constant rank-type constraint qualificati...

In this note we show with a counterexample that all conditions proposed in [Y. Zhang, L. Zhang, New Constraint Qualifications and Optimality Conditions for Second Order Cone Programs. Set-Valued Var. Anal (2019) 27:693-712] are not constraint qualifications for second-order cone programming.

The constant rank constraint qualification introduced by Janin in 1984 for nonlinear programming has been extensively used for sensitivity analysis, global convergence of first- and second-order algorithms, and for computing the derivative of the value function. In this note we discuss naive extensions of constant rank type constraint qualification...

We correct Proposition 3.1 of Ref. Haddon et al. (J Optim Theory Appl 183:642, 2019).

BACKGROUND: Syphilis, together with other sexually transmitted infections, remains a global public health problem that is far from being controlled. People deprived of liberty are one of the vulnerable population. Control activities in prisons rely mostly on passive case detection, despite the existence of affordable alternatives that would allow s...

BACKGROUND: Syphilis, together with other sexually transmitted infections, remains a global public health problem that is far from being controlled. People deprived of liberty are one of the vulnerable population. Control activities in prisons rely mostly on passive case detection, despite the existence of affordable alternatives that would allow s...

BACKGROUND: Syphilis, together with other sexually transmitted infections, remains a global public health problem that is far from being controlled. People deprived of liberty are one of the vulnerable population. Control activities in prisons rely mostly on passive case detection, despite the existence of affordable alternatives that would allow s...

BACKGROUND: Syphilis, together with other sexually transmitted infections, remains a global public health problem that is far from controlled. People deprived of liberty are a vulnerable population. Control activities in prisons rely mostly on passive case detection, despite the existence of affordable alternatives that would allow switching to act...

Environmental variability has a strong influence on marine fish stocks. Thus, management and harvest policies based on deterministic indicators, such as maximum sustainable yield (MSY), may be inappropriate facing such uncertainties. In this study, we investigate the long‐term behavior of a single‐species fishery, whose stock is harvested by severa...

We revisit the optimal control problem of maximizing biogas production in continuous bio-processes in two directions: 1. over an infinite horizon, 2. with sub-optimal controllers independent of the time horizon. For the first point, we identify a set of optimal controls for the problems with an averaged reward and with a discounted reward when the...

We revisit the optimal control problem of maximizing biogas production in continuous bio-processes in two directions: 1. over an infinite horizon, 2. with sub-optimal controllers independent of the time horizon. For the first point, we identify a set of optimal controls for the problems with an averaged reward and with a discounted reward when the...

In this paper, we introduce an approach based on viability theory for designing rebuilding programs for overexploited natural resources. Instead of using the so-called viability kernel, as is usual in the applications of viability theory, we consider the set of sustainable thresholds, which represents the constraints (parametrized by thresholds) th...

In this manuscript we investigate the long-term behavior of a single-species fishery, which is harvested by several fleets. The time evolution of this population is modeled by a discrete time stochastic age-structured model. We assume that incertitude only affects the recruitment. First, for the deterministic version of this model, we characterize...

In previous works CO2 emissions in oil refineries have been studied for the production units planning. In this manuscript the associated CO2 mitigation costs are added to the scheduling of crude oil unloading and blending. Numerical simulations executed on literature cases show that the optimal scheduling may be affected, thus CO2 emissions may be...

In this paper, we give a unified treatment of two different definitions of complementarity partition of multifold conic programs introduced independently in Bonnans and Ramírez [Perturbation analysis of second-order cone programming problems, Math Program. 2005;104(2–30):205–227] for conic optimization problems, and in Peña and Roshchina [A complem...

In this work we study the optimal control problem of maximizing the average biogas production over an infinite horizon. We consider a large class of growth rate functions that depend on substrate and biomass concentrations and we solve this problem for the chemostat model. The obtained optimal control is a autonomous state feedback.

We address the question of mean biomass volumetric productivity optimization, which originates from the simplification of dynamics of microalgae in a batch bioreactor process with light incidence. In particular, the stability of the model is analyzed, some optimality necessary conditions for the nonsmooth optimization problem obtained through the i...

Microalgae culture fed with ammonium may face the presence of nitrifying bacteria. The aim of this paper is to propose and analyze a nonlinear system which represents XCZthe dynamics of these two species (microalgae and nitrifying bacteria) in competition for nitrogen (present as ammonium and nitrate produced by nitrification) in a continuous proce...

In this work, we revisit a problem of optimal control for the maximisation of biogas production in a continuous bioreactor, for which the analytical determination of the optimal synthesis is an open problem. We consider two kinds of growth rates: substrate dependent or substrate and biomass dependent. We propose a sub-optimal controller, as a most...

In this work we propose a stochastic model for a sequencing-batch reactor (SBR) and for a chemostat. Both models are described by systems of Stochastic Differential Equations (SDEs), which are obtained as limits of suitable Markov Processes characterizing the microscopic behavior. We study the existence of solutions of the obtained equations as wel...

This paper is devoted to the study of optimal solutions of symmetric cone programs by means of the asymptotic behavior of central paths with respect to a broad class of barrier functions. This class is, for instance, larger than that typically found in the literature for semidefinite positive programming. In this general framework, we prove the exi...

We address the problem of the optimal control of in situ decontamination of water resources. We review several modeling, simulation and optimization techniques for this problem and their results. We show the benefit of combining tools from finite dimensional optimal control theory and numerical simulations of hydrodynamics equations, for providing...

Two gaps were found in the proof of the main theorems (Theorems 21 and 26) of the paper “On the Aubin property of critical points to perturbed second-order cone programs” [SIAM J. Optim. 21 (2011), 3, pp. 798–823] by J. V. Outrata and H. Ramírez C. In this note both these gaps will be filled. As to the second one, a new technical result will be emp...

We show that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in geological media, there exist equivalent multi-rate mass transfer and multiple interacting continua representations, which are quite popular in geo-sciences. Moreover, we provide explicit methods to cons...

We show that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in geological media, there exist equivalent multi-rate mass transfer and multiple interacting continua representations, which are quite popular in geo-sciences. Moreover, we provide explicit methods to cons...

This paper studies the bioremediation, in minimal time, of a water resource or reservoir using a single continuous bioreactor. The bioreactor is connected to two pumps, at different locations in the reservoir, that pump polluted water and inject back sufficiently clean water with the same flow rate. This leads to a minimal-time optimal control prob...

This paper develops a theoretical framework to assess resources management procedures from a sustainability perspective, when resource dynamics is marked by uncertainty. Using stochastic viability, management procedures are ranked according to their probability to achieve economic and ecological constraints over time. This framework is applied to a...

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MINC (Multiple INteracting Continua) and MRMT (Multiple-Rate Mass Transfer) are mathematical schemes used to modelling transport and difussion in fractured porous media. The main difference between them is the connectivity structure. MINC has a chained type structure (line form) and MRMT has a star-shaped connectivity structure. The goal is show th...

This paper is devoted to the study of a broad class of problems in conic programming modeled via parameter-dependent generalized equations. In this framework we develop a second-order generalized differential approach of variational analysis to calculate appropriate derivatives and coderivatives of the corresponding solution maps. These development...

The paper concerns parameterized equilibria governed by generalized equations whose multivalued parts are modeled via regular normals to nonconvex conic constraints. Our main goal is to derive a precise pointwise second-order formula for calculating the graphical derivative of the solution maps to such generalized equations that involves Lagrange m...

In this note, we correct a mistake in the paper (López et al., J Optim Theory Appl 159(3):741–768, 2013).

This paper studies the bioremediation, in minimal time, of a water resource or reservoir using a single continuous bioreactor. The bioreactor is connected to two pumps, at different locations in the reservoir, that pump polluted water and inject back sufficiently clean water with the same flow rate. This leads to a minimal-time optimal control prob...

In this paper, we analyse the optimality of affine control system of several species in competition for a single substrate on a sequential batch reactor, with the objective being to reach a given (low) level of the substrate. We allow controls to be bounded measurable functions of time plus possible impulses. A suitable modification of the dynamics...

This paper is devoted to the study of the symmetric cone linear complementarity problem (SCLCP). Specifically, our aim is to characterize the class of linear transformations for which the SCLCP has always a nonempty and bounded solution set in terms of larger classes. For this, we introduce a couple of new classes of linear transformations in this...

This paper analyzes feeding strategies in a sequential batch reactor (SBR) with the objective of reaching a given (low) substrate level as quickly as possible for a given volume of water. Inside the SBR, several species compete for a single substrate, which leads to a minimal time control problem in which the control variable is the feeding rate. F...

In this work we apply multi-class support vector machines (SVMs) and a multi-class stochastic SVM formulation to the classification of fish schools of three species: anchovy, common sardine, and Jack Mackerel, and we compare their performance. The data used come from acoustic measurements in southern-central Chile. These classifications were carrie...

This paper establishes a commutation result for variational problems involving spectral sets and spectral functions. The discussion takes places in the context of a general Euclidean Jordan algebra.

In this paper we consider the optimal control problem consisting of feeding in minimal time a Sequential Batch Reactors (SBR) where several species compete for a single substrate, with the objective being to reach a given (low) level of the substrate. Following [8, Gajardo et al. Minimal Time Sequential Batch Reactors with Bounded and Impulse Contr...

We study minimal time strategies for the treatment of pollution in large water volumes, such as lakes or natural reservoirs, with the help of an autonomous bioreactor. The control consists of feeding the bioreactor from the resource, with clean output returning to the resource with the same flow rate. We first recall recent characterizations of opt...

In this paper we introduce a new class, called F, of linear transformations defined from the space of real n×nn×n symmetric matrices into itself. Within this new class, we show the equivalence between Q- and Qb-transformations. We also provide conditions under which a linear transformation belongs to F. Moreover, this class, when specialized to squ...

We develop a theoretical framework to assess sheries management strategies from a sustainability perspective, when the bioeconomic dynamics are marked by uncertainty. Using stochastic viability, management strategies are ranked according to their probability to satisfy economic and ecological constraints over time. The proposed framework is useful...

We characterize the Aubin property of a canonically perturbed KKT system related to the second-order cone programming problem in terms of a strong second-order optimality condition. This condition requires the positive definiteness of a quadratic form, involving the Hessian of the Lagrangian and an extra term, associated with the curvature of the c...

Abstract In the case of small pelagic fish, it seems reasonable to consider harvest functions depending nonlinearly on fishing effort and fish stock. Indeed, empirical evidence about these fish species suggests that marginal catch does not necessarily react in a linear way neither to changes in fishing effort nor in fish stock levels. This is in co...

This paper deals with the control of discrete-time dynamical, monotone both in the state and in the control, in the presence of state and control monotone constraints. A state xx is said to belong to the viability kernel if there exists a trajectory, of states and controls, starting from xx and satisfying the constraints. Under monotonicity assumpt...

This work is devoted to the study of existence and stability results of semidefinite linear complementarity problems (SDLCP). Our approach consists of approximating the variational inequality formulation of the SDLCP by a sequence of suitable chosen variational inequalities. This provides particular estimates for the asymptotic cone of the solution...

Les auteurs présentent une nouvelle classe de problèmes de négociations qui peut refléter les problèmes de durabilité recouvrant des enjeux de nature différentes et des problèmes intertemporels. Chaque porteur d'enjeu s'intéresse à l'évolution d'un indicateur dépendant de l'état du système et des décisions, et cherche à maximiser la valeur minimal...

We study minimal time strategies for the treatment of pollution of large volumes, such as lakes or natural reservoirs, with the help of an autonomous bioreactor. The control consists in feeding the bioreactor from the resource, the clean output returning to the resource with the same flow rate. We first characterize the optimal policies among const...

This paper develops a theoretical framework to assess resources management procedures from a sustainability perspective, when re-source dynamics is marked by uncertainty. Using stochastic viability, management procedures are ranked according to their probability to achieve economic and ecological constraints over time. This frame-work is applied to...

In this work, we study the properties of central paths, defined with respect to a large class of penalty and barrier functions, for convex semidefinite programs. The type of programs studied here is characterized by the minimization of a smooth and convex objective function subject to a linear matrix inequality constraint. So, it is a particular ca...

Apuntes

Some monospecies age class models, as well as specific multi-species models (with so-called technical interactions), exhibit useful monotonicity properties. This paper deals with discrete time monotone bioeconomics dynamics in the presence of state and control constraints. In practice, these latter "acceptable configurations" represent production a...

In this work, we propose an inexact interior proximal type algorithm for solving convex second-order cone programs. This kind of problems consists of minimizing a convex function (possibly nonsmooth) over the intersection of an affine linear space with the Cartesian product of second-order cones. The proposed algorithm uses a distance variable metr...

This paper is devoted to the study of the global asymptotic behavior of a model of chemostat with an arbitrary number of competitors following a Monod law on their specific growth rate functions. The model incorporates discrete time delays in order to take into account the delay in the conversion of nutrient consumed to the viable biomass. In this...

This note deals with a harvesting model for a single stock fishery. In the case of small pelagic fish it seems reasonable to consider harvest functions depending nonlinearly on fishing effort and on fish stock. Empirical evidence about these fish species suggests that marginal catch does not necessarily react in a linear way to changes in fishing e...

We consider the optimal control problem of feeding in minimal time a tank where several species compete for a single resource, with the objective being to reach a given level of the resource. We allow controls to be bounded measurable functions of time plus possible impulses. For the one-species case, we show that the immediate one-impulse strategy...

We consider the optimal control problem of feeding in minimal time a tank where several species compete on a single resource. We allow controls to be bounded measurable functions of time as well as impulses. For the one species case, we extend former results given by Moreno to the framework of impulse controls. For the two species case with increas...

In this paper we present penalty and barrier methods for solving general convex semidefinite programming problems. More precisely, the constraint set is described by a convex operator that takes its values in the cone of negative semidefinite symmetric matrices. This class of methods is an extension of penalty and barrier methods for convex optimiz...

We discuss first and second order optimality conditions for nonlinear second-order cone programming problems, and their relation with semidefinite programming problems. For doing this we extend in an abstract setting the notion of optimal partition. Then we state a characterization of strong regularity in terms of second order optimality conditions...

This work deals with a number of subjects on nonlinear semidefinite programming (SDP). In the first two chapters, we consider the problem from an algorithmic standpoint while in chapters 3 and 4 we study theoretical aspects, in particular, giving a perturbation analysis of the problem. In the first chapter we develop a global algorithm that extends...

In this paper we propose a global algorithm for solving nonlinear semidefinite programming problems. This algorithm, inspired by the classic SQP (sequentially quadratic programming) method, modifies the S-SDP (sequentially semidefinite programming) local method by using a nondifferentiable merit function combined with a line search strategy.

Le but de cette thèse est d'étudier des différents sujets de la programmation semidéfinie non linéaire(SDP). Ainsi, dans les deux premiers chapitres nous presentons certains aspects algorithmiques, dans les chapitres 3 et 4 nous travaillons sur des aspects théoriques comme l'analyse de perturbations de ce problème. Le premier chapitre développe un...